How secure is it to receive an offer of post-doc position in email?
An unofficial offer is typically a notification of intent to make a formal offer, and I believe not legally binding.  This is not to say that an offer in email is not official and cannot be legally binding---but according to you the offer is unofficial.  Even if it is legally binding, having to take a university to court to secure a position does not sound like a productive way to start a postdoc.

Assuming the postdoc is completely funded from a grant on which this professor is the PI, in all likelihood the only way this would not turn into a formal offer is if the professor changes his mind or is somehow incapacitated.  Also, formality standards of offers can vary.  Anyway, if you are worried about it, I suggest you ask about the terms (if you have not received them) and when you can expect a formal offer.