Mr. Whittaker is a Time Lord.
The Imagination Station is his TARDIS. Because a properly-working TARDIS has a chameleon circuit, this would explain why it has been known to take on different appearances through the history of the show (having been described as resembling "a helicopter cockpit", "a hot water bottle turned on its side", etc.) The Imagination Station is a time machine of sorts - even though Whit claims that it's only a simulation, it has been established that injuries sustained on Imagination Station adventures can carry over to real life, suggesting that it may be real, as it would be with traveling in a TARDIS.
Mr. Whittaker has had three regenerations (the character has been played by three different actors). His first regeneration happened when he was in the Middle East on the archeological dig. This is also why, when Eugene and Jason went there to find him, Eugene didn't recognize him at first. (It wasn't pointed out that Whit looked any different, because Eugene would have known that he was a Time Lord and thus didn't have to draw attention to this fact.) His second regeneration was a quieter affair, and it explains why his voice is now much different than his previous incarnations. (It coincidentally happened during his regeneration that the second Whit's voice was the same as the first Whit's.) His regenerations would also account for why there are subtle personality differences between his three portrayals.
The people who have worked at Whit's End are his companions, but Connie and Eugene are the longest-running companions. Whit's End may also be a TARDIS, as it is suggested (even by the producers of Adventures in Odyssey) that it may be Bigger on the Inside.