how long did homer work at teh power plant for

Ten years, the same day Bart was born.

With all the times he got fired and the over 100 jobs he has had since Season 1 haha, I don't think we will ever know the exact period of time he has worked continously at the plant. He did start working when Bart was born, but since the show is on a floating timeline, the exact number of years is hard to determine :)