Where does "otay" come from?
Solution 1:
When I use it, I'm deliberately emulating baby talk. It doesn't really mean anything different than "okay" (pronounced properly); it's just a way to be, I dunno, cutesy.
I didn't know about the Little Rascals/Buckwheat connection, possibly because I grew up without a TV. I'm sure Buckwheat contributed to at least some of the popularity of "otay", and possibly I absorbed it from someone who (unbeknownst to me) was imitating the TV show, but it's also possible that this is something that each generation/school/user invents anew.
Solution 2:
"Otay" comes from The Little Rascals (a.k.a. "Our Gang"), a 1920's comedy series featuring a variety of child actors, in particular one called Buckwheat, who had a bit of a lisp or perhaps a minor speaking impediment at the time. This character was later caricatured by Eddie Murphy on Saturday Night Live, who made a big production out of the practically unintelligible "Buckwheat dialect", including "Oh-Tay!" specifically as a catchphrase.
Solution 3:
I believe it comes from the character of Buckwheat in the old TV show The Little Rascals.