Fastest Jack of Trades (10/15/20 quick skills) - can obviously upgrade anything but this should be doable for any level.  This is just a resource for limited time or if you are just trying to knock out a few extras...

CITADEL - one stop - 7 skills! don't need to bring anything but exp bonus items if you plan to cap!
Smithing
Cooking
Summoning
Firemaking
Cooking
Crafting
Woodcutting

Tele to easiest fishing spot (if you do Catherby - can farm fruit tree too) - most of them have trees nearby - should have most supplies on tool belt
Fishing
Woodcutting - cut 2 trees
Fletching - fletch one log
Firemaking - burn one log
Cooking - cook fish (might need an extra fish if burning is an issue)

Tele to Varrock lodestone - pickpocket guards - attack with range, melee (and magic if you don't use explorer's superheat) - I keep a chargebow and a staff with free spells for this
Thieving
Strength
Attack
Defence
Range
Hitpoints
Prayer
(Magic)

Superheat - if have explorer's ring or magic level and want to use runes
Magic
Smithing

Divine Locations - recommend World 2 Burthorpe bank - can get any of these with the appropriate skill levels / is not directly from location but can be a follow-up
Hunter
Woodcutting / Firemaking
Mining (with superheat - Smithing/Magic)
Farming / Herblore
Divination
Fishing / Cooking

Miscellaneous Others
Hunter - catch any impling you see - remember lower level implings spawn higher level ones - so if everyone catches the baby / young implings there will be more higher level ones to go around!
Construction - if have Prif - harp which also gives crafting
Agility - can be a shortcut or a course or clockwork mouse
Slayer - Jade Vine or Task
Herblore Cleaning or adding an herb to a vial of water (do this every day and you are set for training!)
Farming even just weeding works
Divination - Falador Lodestone is really near a div spot if you are not particular about levels
Runecrafting - Wicked hood - either tp to altar or runespan

For Just Starting Out or Really One Stop Shopping for all except Slayer, Construction (although you can do the statue once a month), Runecrafting and Divination.
BURTHORPE:
Fletching can visit tutor as well as just fletching a random thing from a tree
Firemaking
Woodcutting

Cooking
Fishing (near hunting tutor)

Strength - wolves, rabbits, trolls...
Attack
Defence
Hitpoints
Ranged
Magic
Prayer

Hunter - can get supplies from tutor

Smithing
Crafting - bowstrings, hides, clay in mine
Mining

Thieving pompous merchants
Agility - course to the North
Herblore - can get supplies from tutor
Farming  - can get supplies from tutor
Summoning - can get supplies from tutor

Notes: I don't think you can get Dungeoneering credit for Jack of Trades unless they updated it.
  If you are high enough level Prifddinas has it all too although sometimes not as fast but much better exp.
  Temple Trekking usually can cover a bunch of skills fast too.

never done these before :o
What's the time limit and what's the xp reward?

Jack of Trades is a Tier 2 aura - there is a Master Tier 3 version and a Supreme Tier 4 version.  You get 3 hours that it is active - it used to have a 24 hour cooldown (which drove me crazy) but now it resets with the reset.  Anyway, for the tier 2 you can complete 10 different skills (1 exp is enough but lamps don't count any more) , for tier 3 you can do 10 or 15, and for tier 4 you can do 10, 15 or 20 different skills.
For 10 skills you get:
1.5*(x^2-2x+100) experience (where x is the level of the skill you are getting experience in - it is straight experience not bonus)
(148.5 points level 1, 3750 points level 50, 14,554.5 points level 99)
For 15 skills:
2*(x^2-2x+100) experience
For 20 skills:
2.5*(x^2-2x+100) experience

Also you can't start the aura if you have not claimed the previous reward book.  You can claim it in Varrock (outside the place you buy battle staves), in Burthorpe (East of agility course), and in Prifddinas (SW of center Room)

I have the tier three version (15 skills) what I do is

1 Runecrafting with wicked hood teleport to altar.
2 Tele to daemonheim bank rune pouches/runes and craft a sign of the porter for Divination exp.
3 Tele to Taverley loadstone and pickpocket a Pompous merchants (they are near the loadstone)
4 Pick flax north of the loadstone for farming exp
5 Fish a crayfish on the lake
6 Cut two logs
7 Get and set a Bird snare by the Hunter tutor (it is free)
8 Get a grimmy guam from the herblore tutor and clean it (it is free)
9 Ground the clean Guam for cooking exp
10 Burn one of the logs
11 Cut one of the logs for Fletching
Loot the bird snare (it will 99% of the times catch a bird if you have high hunter level if it fails set it again and do the next 2 skil)
12 Craft a bow string with the flax picked earlier
13 Mine one cooper and tin ore
14 Smelt a bronze bar
15 Cross the first obstacle on the tutorial agility course.

I had never thought of using the citadel

There are higher tiers?

Yeah - I didn't know either but the higher tiers are great!

Nice!

I have the tier three version (15 skills) what I do is

1 Runecrafting with wicked hood teleport to altar.
2 Tele to daemonheim bank rune pouches/runes and craft a sign of the porter for Divination exp.
3 Tele to Taverley loadstone and pickpocket a Pompous merchants (they are near the loadstone)
4 Pick flax north of the loadstone for farming exp
5 Fish a crayfish on the lake
6 Cut two logs
7 Get and set a Bird snare by the Hunter tutor (it is free)
8 Get a grimmy guam from the herblore tutor and clean it (it is free)
9 Ground the clean Guam for cooking exp
10 Burn one of the logs
11 Cut one of the logs for Fletching
Loot the bird snare (it will 99% of the times catch a bird if you have high hunter level if it fails set it again and do the next 2 skil)
12 Craft a bow string with the flax picked earlier
13 Mine one cooper and tin ore
14 Smelt a bronze bar
15 Cross the first obstacle on the tutorial agility course.

Jack of Trades is a Tier 2 aura - there is a Master Tier 3 version and a Supreme Tier 4 version.  You get 3 hours that it is active - it used to have a 24 hour cooldown (which drove me crazy) but now it resets with the reset.  Anyway, for the tier 2 you can complete 10 different skills (1 exp is enough but lamps don't count any more) , for tier 3 you can do 10 or 15, and for tier 4 you can do 10, 15 or 20 different skills.
For 10 skills you get:
1.5*(x^2-2x+100) experience (where x is the level of the skill you are getting experience in - it is straight experience not bonus)
(148.5 points level 1, 3750 points level 50, 14,554.5 points level 99)
For 15 skills:
2*(x^2-2x+100) experience
For 20 skills:
2.5*(x^2-2x+100) experience

so you get that xp for all skills or you pick one skill?

so you get that xp for all skills or you pick one skill?

You pick one skill, can be any skill.

Here's what I do. It takes me like 3 minutes to complete a run.
**Supreme JOT Aura
This all takes place in Burthrope
1. Cut uncut Jade
2. Make Energy potion
3. Run south and go into mine. Then mine one Copper, one Tin ore
4. Exit mine and make a bronze bar
5. Smith Bronze throwing knives
6. Cut 2 logs
7. Purchase free Bird snare and place it
8. Run a bit south and fish one crayfish
9. Run west and rake potato patch
10. Kill cow with bronze throwing knife
11. Kill cow with Balanced melee attack
12. Go retrieve bird snare.
13. Bury bones
14. Fletch bow
15. Make fire
16. Cook raw fish
17. Run south and pickpocket a NPC
18. Wind, release, and pick up Penguin
19. Teleport to Varrock
20. Collect XP reward

That looks great!

Here's what I do. It takes me like 3 minutes to complete a run.
**Supreme JOT Aura
This all takes place in Burthrope
1. Cut uncut Jade
2. Make Energy potion
3. Run south and go into mine. Then mine one Copper, one Tin ore
4. Exit mine and make a bronze bar
5. Smith Bronze throwing knives
6. Cut 2 logs
7. Purchase free Bird snare and place it
8. Run a bit south and fish one crayfish
9. Run west and rake potato patch
10. Kill cow with bronze throwing knife
11. Kill cow with Balanced melee attack
12. Go retrieve bird snare.
13. Bury bones
14. Fletch bow
15. Make fire
16. Cook raw fish
17. Run south and pickpocket a NPC
18. Wind, release, and pick up Penguin
19. Teleport to Varrock
20. Collect XP reward

Wish they had a like button on forums sometimes!

I tend to vary partially depending on what I want to do - but typically I have been going to Prif and (depends also on VOS):
My method in probably not efficient but I never claimed to be - just like to know what my options are

Crwys
1,2 - I cut 2 magic logs *full disclosure sometimes more - and fletch one (woodcutting and fletching)
3,4,5 - I farm a barberry bush and snapdragon - and clean it (farming, agility and herblore)
TP to center of Prif
6,7 - add magic log to bonfire and cook whatever raw fish I have in bank (firemaking and cooking)
Ithell
8,9 - mine crystal flecked sandstone - and make potion bottles (crafting and mining)
10 - tune harp (construction)
11 - thieve (thieving :O )
12,13 - stop at bank chest and superheat 9 iron and 18 coal (smithing and magic)
Then I usually tp to Varrock lodestone bringing abyssal whip and Kayla's chargebow and kill guard (I try to hit range and melee one guard)
14,15,16,17,18,19 - kill guard and bury bones (strength, attack, defense, ranged, hitpoints, prayer) * usually do this on way to picking up battlestaves but the prices bite right now! - anything with bones or ashes would work - sometimes go straight to world 2 Burthorpe and get wolves south of bank

If I see an impling on the way I am done
Otherwise I head to World 2 Burthorpe and do div locations (actually I do this anyway)
and get one for #20:
  hunting
  divination
OR  fishing
Occasionally I do runecrafting with magic hood - or summoning at tutor instead...