A friend of mine has rented a room out in his house to a evil woman and her teenage daughter. My question is how can he evict her without a signed rental lease?

First I hope a lesson learned that they always need a written rental agreement that spells out what can and can not be done.
But assuming they are paying monthly, she has to give them a 30 day notice that they have to move. ** unless it is for non payment of rent then a shorter notice to pay or quit is allowed.