I'm doing a MBA and have a valid I20. The college is traveling to Estonia for 7 days. But my F1 visa has already expired. Can I still travel and have entry to the USA to continue my MBA with an expired F1 visa.
You cannot re-enter the US without a valid visa (there is an exception for Mexico and Canada). You can however use the I-20 to get a new visa issued from the consulate. It is better to do it from your home country, but you can consider trying from Estonia as well if you can give them an acceptable reason for why you are doing so.
You should consult your university's international students' office for better advice on where to apply and when.