Halo 1 and 2 are on PC, and they are hinting at X360 on PC compatibility, so Halos 3 and 4 are at least on the table..
Halo 4 was a bit of a departure from the original trilogy, as was to be expected. We can't expect a multi-million dollar game series to keep the same gameplay concepts for 15 years, spanning 3 hardware generations. The series has evolved, but I wouldn't say for the worse. I really liked Halo 4's story.
I won't get Halo 5 for at least another month, but I've heard the story is polarizing. Usually this means it's good, a bland story is just boring. Quite frankly, in comparison, the original trilogy was boring.
I don't know why you're biased against the Xbone.. But if you like Halo, just bite the bullet I'd say. It's not like the PS4 is any better.. Any decent PC puts the two to shame.