Most Americans I know use the latter, in which the r and l do not have a vowel between the two.
Are you from the southeast US? I've always heard "squih-ruhl". You also mentioned pronouncing "owl" like Al, which doesn't sound right to me either.
I'm guessing these are the same people who pronounce "terrorist" almost the same as "tourist"
Pacific Northwest here. I pronounce "squirrel" as "squirl".
It gets worse. There's a town, "Sequim". The way you know someone isn't from around here is if they pronounce it "See-quim". It's actually pronounced "Squim".