Question: I was wondering, which is the correct sentence in this case.

你的生日是几月几号？ or 你的生日几月几号？ (without 是) 

Also can I omit 的 in this case?

Answer: 
The line without 是 is not a correct sentence because it doesn't have a verb. It's fine in spoken language but should be avoided in formal writing.

In this sentence, it is fine to omit 的 in spoken language, too.

To recap,

> 
> 你的生日是几月几号？ Grammatical, fine for both formal and informal usages.
> 
> 
> 你的生日几月几号？Not a complete sentence, only used in spoken language.
> 
> 
> 你生日是几月几号？Whether it's grammatical is arguable. Regardless, it's common in spoken language.
> 
> 
>
As a general rule, if you use a 是, you should have a corresponding 的.

For instance:

这是很好吃的！
我今天是很忙的。
你今天是怎么样的呢？

The Chinese, though, favor saying less to get the same meaning across. So when speaking, sometimes the 是 and/or the 的 will not be spoken.