Agilineck, the Girafarig: Must know Agility and Baton Pass, must never leave team [Never used one of these before XD]
Combee.Jr: Kricketot: Must evolve at Lv 16. Must be the first one found in the wild. Must know at least one STAB move as soon as it can learn one, and one Non-STAB.
Sergeant, the Piplup: May not evolve until it KO's a Gym-leader's pokemon with Fury Attack. No further evolution until it acheives the same feat with Drill Peck
Steelix: Must know Earthquake ASAP. Must use Earthquake every Double Battle. If it dosen't solo Bastoodon, it can't be used against Volkner, Flint, Aaron or Cynthia. Cannot Evolve until after Maylene [Can you even get the Metal Coat before then?]
Gligar: Doug: Cannot have items used on it, until the Elite 4 is reached. Cannot evolve unless it KO's Candice's Abomasnow. Can use Hold items.
EDIT:
Riolu from Riley: Evolve ASAP, Teach Aura Sphere. Once this is learned, physical attacks become disabled [So No BP'ing Agility to it and sweeping like no tomorrow with Swords Dance Lucario]
Let the challenge Begin!