How does Ivar's handicap in Vikings work?

I don't think that the show ever states exactly what Ivar's disease is. In season 4, episode 11, when Ivar is trying to sleep with a slave, his deformed legs are shown for a moment, and they look, (to me) like he was born with clubbed feet. That would explain the "twisted" appearance of his feet. It doesn't look (again, to me) like his actual legs were deformed, just underdeveloped, which would make sense since he crawled and sort of dragged his legs around for most of the episodes in season 4. He wasn't paralyzed by any spinal issues, so his legs probably had more mobility than we might assume, since the problem was not being able to stand on his deformed feet, instead of not moving his legs. One of the diseases that I have heard mentioned is brittle bone disease, which makes bones very easy to break. Ivar's deformity could be from his bones breaking quite a bit, (which could happen in the ancient world). Some people who suffer from brittle bone disease also have a bluish tint to the whites of their eyes. In season 5, episode 8, Ivar is on the battlefield, and he asks his brother Ubbe how blue his eyes are. When Ubbe replies that his eyes are very blue, Ivar states that as a child, he knew that when the whites of his eyes were very blue, he knew that he was in "great danger of breaking a bone." So, he may suffer from brittle bone disease, even though the Viking series has taken a few liberties with how realistic Ivar's condition is. I hope that helps.

I would say that the nickname Boneless in the first place is, of course, derived from the look of his legs and people in that time couldn't definitely know about something like a genetical disease he was born with, they would not ever even think about it in concepts we think about it today. They may have associated it with a religion, just born in weakness... We are talking here about extremely militarized society.

About his ability to walk, I would say that the creators wanted to somehow "normalize" his character. It was pretty awkward for viewers to see someone crawling all the time, mostly during non combat scenes and interactions. In combat, they gave him this super war carriage and in non combat scenes they gaved him some kind of a replacement that looks "medieval", because is maded from an iron and looks like a typical medieval concept of equipment you can see in most movies... It's of course completely unrealistic but hey, we are not talking realism in here...