Its very similar to both dog and dawg, however this variation of the word has a different pronunciation. Unlike dog and dawg, doeg is pronounced with a strong annunciation on the "o" syllable. It sounds like it is spelled doooooeg or doe-g, rather than simply dog.
In the movie I Love You Man, Peter Klaven calls his friend SydneyFife on the phone and says, "I'm workin' like a doeg."
It's a slower way of saying dawg by just using a lazy slower deeper voice kinda like saying doug but instead comes out as doewg usally used by fake ass tricks and playa's
Yo Doewg lets roll to the store and gets some monsta's i got them munchies and lets get some donuts
girl :bae boy:what
girl: im pregnat my parents are gonna kill me
boy: damn, i dont know if thats my baby because you a little thotiana
girl: they were when we were on breaks
boy:they? we were on break once
girl:thats not important right now
boy: thats not my child bye doyg