I've seen threads like this before where people attempt to make the "best" champion with Blitzcrank's Q, Karthus' R, etc. However, I think it'd be cool to do something similar, but go for a super themed champion. We will not consider champion passives or base stats, but we will try to build a champion that has some over-the-top characteristics about it. Here's my example:

Jumpy, the Escape Artist

Q - Shaco's Deceive
W- LeBlanc's Distortion
E - Ezreal's Arcane Shift
R - Kassadin's Riftwalk

Go!

OP, The over powered

Q - Naut's Q
W - Karthus' W
E - Garen's E
R - Amumu's R

Garen's final form, The final boss of the world

Q-Darius
W-Katarina
E-Garen
R-Wukong

Ooh, sounds fun. Though, you forgot to let them pick a passive as well.

Marco, the Merchant Prince
Passive - TF's Loaded Dice
Q - Gangplank's Parely - - - Exactly what is says in the tin
W - Gangplank's Remove Scury - - - Reflavor as top of the line healing potions. Maybe allow it to be used on allies in a short range.
E - Ashe's Hawkshot - - - Identical. Maybe shorten range.
R - Teemo's Shrooms - - - Slightly wider vision. Lessen damage. Reflavor as Discount Wards.

I buy any item I want. And fast!
Key to balancing would be relatively poor scaling. Sounds like a *****in support though.

Q - Alistar's Headbutt
W - Blitzcrank's Rocket Grab
E - Vayne's Condemn
R - Nautilus's Dredge Line

Tristana's passive
Nasus's Siphoning Strike
Kog'maw's Bio Arcane Barage
Kayle's divine reckoning.
Twitch's Spray and pray

Nasus may have had trouble farming his Q, but only because he was melee.
At 2000 range, I think he can manage.