There are two aspects involved here.
1. Can you claim rent for last 15 years: it might be difficult to prove, that there was oral agreement to stay with/out rent. However, if ever, the institution paid any amount/transferred some amount, then you can show that they were supposed to pay. or can check if any communication from your father's phone to any of the parties, etc to see if any discussion on rent took place.
2. Can you from today claim rent: Yes, you can. you being the new owner of the house, can make a new agreement and charge them rent or else ask them to vacate the premises. Either ways.
So contact them for new rent agreement. If they deny, then send them eviction notice and then the legal course.
For further queries, you can contact me at firstname.lastname@example.org
Sir, I'll provide you certain legal suggestions, but for that i need to ask certain questions from you. For any further assistance, feel free to contact me on my e-mail "email@example.com"
Shubham Pabbi & Associates