Eddipus is the normal American English pronumciation. EEdipus sounds hopelessly stuffy and Brrritish.

It is from Greek - how would it sound in the original?

Love Tom Lehrer, and it makes me sad that so many people now have never heard of him.

"I hold your hand in mine" and "The rose between your teeth" and "Life is like a sewer" and "When Mozart was my age..." once got guffaws and belly laughs. Now they gte puzzled looks and require explanation. Getting old is tough.

So keep singing his songs!