From what I've seen of interviews, the Captain Beefheart comparisons don't end with the music. Ornette is a weird guy who seems to live in his own universe, and he has trouble explaining his alien concepts in mere words.
As near as I can figure "harmolodics" means that the harmony is built up from a pile of melodies played on top of each other, rather than using "chord theory" -- the "souped-up Dixieland" metaphor isn't a bad way to think about it.
But I think it's also a whole lot of individual idiosyncracies that don't necessarily translate to anyone else -- playing harmolodic jazz is pretty much synonymous with being a member of Ornette Coleman's group.
Though Royal Trux once claimed to play harmolodic music . . . (do you believe them?)
;-)