Most eccentric role?

I don't think so. That was his weirdest. Ironically it came right after The Graduate and he was briefly America's heart throb. So teen girls showed up on the Midnight Cowboy set and saw this homeless bum.
Anyway, Dustin is one of my favorite actors. It sucks that he became a victim of Me Too false accusers like many others.

Hook was more flamboyant, maybe. Ray Babbit might not be "weirder" (I'm not sure I'd put mental health and "weird" in the same column; that seems narrow-minded), but he's certainly full of affectation.

For my money, though, it's hard to get more eccentric and odd than the cape-wearing drama critic he plays in Lemony Snicket's A Series of Unfortunate Events. Out of NOWHERE Dustin Freakin' Hoffman shows up wearing a cape and just watches the show. It's not that Hoffman is doing anything strange, it's just that the whole thing is so bizarre and inexplicable...

His portrayal of an existential detective (partnered with Lily Tomlin) in I Heart Huckabees comes to mind as well, although the strangeness there is so much in what he is saying rather than how he is saying it.

Mumbles in Dick Tracy was fun to watch, but not really a tour de force role per se.

Yeah... Ratso is hard to beat. Lenny Bruce was somewhat eccentric too, I think!

Roald Dahl's Esio Trot

That came to mind immediately for me. Probably one of his more obscure appearances, it's a BBC production based on the Dahl book (obviously) where he plays a retired bachelor who falls for his widowed downstairs neighbour (Judi Dench) and woos her with tortoises.

Quirky and very cute, definitely worth a watch if you can find it.