ROFL at Jim and Jack, Barack Obama and Bustados and Joan! DD, now 5.10, has always had imaginary friends. Currently we have Abigail (imaginary sister), Oon and another sister whose name I forget but that pair are very badly behaved, and several imaginary ponies.
My favourite was 'Fighty the Boy'. She was about 3 when he appeared. We'd hear her having almighty rows with him. Apparently he was appallingly behaved. However he met a sad end when, 'someone accidentally sat on him and squashed him flat.' Poor dd was incosolable, 'as he had just become Good the Boy,' proving that only the good die young, I guess. She brought him back to life again by 'punking [pumping] him up', whereupon he moved to Australia and was never heard of again.
All of these friends can appear at will, but are pretty much guaranteed to appear when she is in the bathroom - to the extent that dh and I now wonder if there is a portal in there.
MIL thinks dd is deranged, but I support the 'sign of intelligence' theory. (Conclusively proved by MIL's counter-arguments, I feel. )