Haven't we been taught that sör is same as sört?
Sört is in accusative, as it's the direct object of the sentence. Sör is in nominative, you would use it as subject: "A sör finom." -- "Beer is tasty."
My grandma says "Igen akarok sört" should have worked.. is that correct?
Yes, that's correct. It's the literal translation.
Using "kérek" is a more polite and more common way to ask for something.