If you use exterior, you will need to wait much longer before introducing birds since this paint typically contains toxic chemicals to prevent mold and mildew - very bad for birds to breathe! Gloss or semi-gloss interior paint would still be washable. There are no standards for "gloss" or "semi-gloss" so check paint chips for different manufacturers to compare. We've always had very good results using Glidden, and their paint tends to have low VOC (volatile organic compounds which produce strong odors).
What I've done is to paint a loose chunk of wood when I paint the coop and use that to check odors. Have it next to you for several hours while you are on the computer or watching TV. Remember that your birds are going to be exposed to the fumes in a confined space overnight and they have more sensitive respiratory systems!