Vai embora

It changes a bit if you are talking about Portuguese from Portugal or from Brazil.
In Brazil, they usually say "Eu preciso ir embora".
If you are in Portugal, you realise that we say "Eu tenho DE/QUE ir embora". Using DE or QUE it doesn't change the sense of your sentence.
However, using QUE for this sentence is incorrect, because you have to do something= Ter DE fazer alguma coisa. The unique way to use QUE correctly is in other way: "Eu tenho que fazer...". This means "I have lots of things to do..."

As you can see, the difference between using QUE and DE is...if you say what are you going to do, you use DE. Finally, if you just want to say "Oh, I have so many things to do right now!" -> "Oh, tenho tanto que fazer agora..."