My father has a family of renters who are not keeping with the rental agreement however, they have a 'medical needs' infant in the house with documentation allowing them to be late on any number of bills and no recourse can be taken. Can they be evicted under Oregon state landlord/tenant laws?

This one is a very difficult question, but "medical needs" do not allow folks to not pay their bills in full. They can be late, but your state law tells you this cannot be an ongoing problem. Your Dad should take his tenants to the local small claims court immediately. He should first give them written eviction notice telling them to be out in 30-days. I'm certainly not aware of any laws, even in the very liberal state of Oregon, that enables or otherwise encourages late rent payment and simultaneously prevents the landlord from taking necessary action. Why hasn't your Dad seen an attorney? The first visit is always free for goodness sake. By the way, Dad needs to be very sure he is a good landlord before he takes any action - again, he needs to see an attorney right away and quit fooling around with this stuff.

... I'm certainly not aware of any laws, even in the very liberal state of Oregon, that enables or otherwise encourages late rent payment and simultaneously prevents the landlord from taking necessary action. ...

Nor am I. If there were, I would expect it to be found in this statute:

ORS 659A.145 (http://www.leg.state.or.us/ors/659a.html)Discrimination against individual with disability in real property transactions prohibited; advertising discriminatory preference prohibited; allowance for reasonable modification; assisting discriminatory practices prohibited.
I see nothing pertaining to that issue there.

They may often be given a extra month to find some place else. But you will want an attorney to do the eviction paper work and represent you in court