The answer is luggage. Orcus had to pack his suitcase.
Even when manifested on the Prime Material, Orcus is still a creature of the Abyss. He has to pick and choose what to pack for his trip. In the case of the OotA stat block, he came loaded for a certain type of fun. He knows that he's eventually going to get sent back to the Abyss; he's got certain goals while he's here, this time, though. Maybe those goals will result in him being able to bring a bigger suitcase, next time. Who knows? Who really cares? It's an excuse for future plot devices, and helps to reconcile the absurdly different stat blocks that have occurred over the years.
When Orcus is acting as a Warlock Patron, he's got a totally different game plan and set of bags. Really, he knows the trip is going to be pretty short, so he just brings carry-on. It's some darn impressive carry-on, though. No physical form, to speak of, but he does get to pack the tools he needs to empower an agent (a.k.a. minion) on the Prime. Once that task is done, he packs up and goes home, like some sort of fiendish jet-setter with a private plane.
Additionally, Orcus is such a magnificently potent entity that his "being" (I hesitate to use the word "soul" for Orcus) isn't really concentrated in one spot. His avatar from OotA doesn't really have any knowledge about what the rest of his consciousness is doing -- his core consciousness may even be in OotA, with and Warlock vassals essentially getting automated support. You still can't fully destroy him by killing the avatar. If you found him on his home plane, you probably couldn't destroy him in a single battle. It would be like tracking down Voldemort's horcruxes until you found every last repository of his being.
For other patrons, like the elder fey from the PHB or elder wyrm I added in my game, the same principle applies, even if the patron exists primarily on the Prime. Their stat block doesn't really give the whole picture. Sure, it tells you what they can do at that moment but it isn't their entire arsenal. The Oberon has his essence slightly diffused and may only be able to gather up a portion of it at a time, but could appear in any number of guises. The elder wyrm is more like a wizard who can reconfigure his spells, but can be killed if caught with his guard down; thus the standard stat block that gives them the best chance of survival for most circumstances, but will give some power to others in rare occasions.
As far as the Great Old One goes.... They really don't even have stat blocks because they play by seriously different rules.
