When I type ' or " on my Mac (OS X 10.7.4) it underlines it and depending on next symbol treats the combination as a special character (for example ä for " + a).
How can I turn that off?
Sounds like you are using a foreign input source. You should go to System Preferences -> Language & Text -> input and make sure you are using the correct language.
However this is not a programming question, so this post will probably get removed.