What I mean is that if I transfer a Jolly Double-Edge Glalie from LeafGreen, can I not use it in wi-fi battles in ORAS at all, or can I just not use it in official tournaments and rating battles?
Yes Its perfectly legal to use Pokemon with a tutor move from a previous gen. Just because it has a previous gen tutor move doesnt mean it is illegal. Softboil Clefable can only come from Gen III move tutor and its used all the time.