If my adult son, his wife and two children live in my home for two years can the financial support I gave be filed on my income taxes?

Not unless you provided more than half their support.

Only if the adult son were NOT working could you claim the adult son; same for his wife.

Now, if you are providing more than HALF of the total supprot for the children, even if the parents ARE working, you CAN legally claim the children, but, for practical reasons, you will need the cooperation of the parents.