If you don't mind instrumental songs, I picked up a random polka album at a thrift store a while back which contained a few fun "American" polka songs, including "COON DOG POLKA" (written by Kansan Rex Ulmer in 1976). Very fun, but instrumental, and I note you were asking for songs with English lyrics.

Not exactly well-known, or beer-related, so admittedly not the best Oktoberfest song, but it is alcohol related, and it is a fun one: the JACK DANIELS WALTZ. The album I got this from (Just For You Vol. 2 by Larry's Concertina Band, from Minnesota) didn't include an attribution, but some searching has shown it was probably written by a Jeffrey D. Talmadge in 1980 (entry PAu001383536 / 1990-06-21 at the US Copyright office); I believe this is the same Jeff Talmadge. Anyhow, below is my transcription of the lyrics from the Larry's Concertina Band recording; additionally, see the dots (page 1, page 2) from someone online; they sound pretty close (if basic) to me, though there are some symbols related to, I believe, concertina playing which are foreign to me which may elucidate something to the more well-read. If you like it, PM me and I'll send you a recording.

JACK DANIELS WALTZ
(Jeffrey D. Talmadge)

Well, it's time for just one drink, so, down the hatch it blows
I don't need no chaser, it's smooth past my tongue as it goes
Now my weakness is Jack Daniels, and he's been good to me
All I need is one little swallow just to keep me company
Now I don't care to be lonely so why don't you come along
Our Jack will keep us company til the bottle is all gone