Is it okay/common practice to reuse reference letters?
In the US, this practice essentially can't happen, because letters of reference are almost never given directly to the student—instead, the referee submits the letter directly to the requester. So you would have to ask your referees to submit the letter again on your behalf.

If you're in a country where the norm is to give a letter of reference directly to the applicant (such as Germany), the letter is usually given out without a target recipient, and is therefore much generic. In such cases, you do not need to request permission to reuse the letter, as it is already designed for such use. 

If you're in doubt, just ask the person who wrote you the letter. Most people will want to update a letter, particularly if it's several years old.