If one family rents a home is it legal for the renter to rent out rooms at the same house for there profit? basically strangers?

Review the terms of the lease. See whether it permits sub-leases. If the lease is silent as to sub-tenants, then the landlord's argument would be that the lease agreement is for the named tenant only. The tenant would likely argue that the named tenant is responsible for the rent payments and the upkeep of the property regardless of whether it is subbed out.
I'm not a landlord/tenant practitioner; so I may be overlooking statutes and caselaw on point. My advice, then, is for you to sit down with a real estate lawyer in your area to go over your concerns.

Dennis Phillips, Esq.
www.inawreck.com. Negligence is no "accident" (TM)
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