What you can do is covered by the Residential Tenancies Act, esp. part 3. The tenant is not totally free of responsibilities: "The tenant is responsible for ordinary cleanliness of the rental unit, except to the extent that the tenancy agreement requires the landlord to clean it". The act enumerates allowed terminations of a lease for cause, and while damaging a unit is a cause, violating the requirement to keep things clean is not, that is, it does not say that you can evict them for having a dirty place (assuming it is not an actual health or safety hazard). There is a form (N-5) which you would fill out to officially give notice to the tenant, indicating an intent to evict, but "the place is dirty" is not in the list of causes, and you are required to explain in detail the "damage" caused by the tenant. It is not prohibited to cite section 33 of the law (the cleanliness clause). A tenant may avoid eviction by complying with the request within 7 days.
You are allowed to enter the unit to show it to prospective tenants, with 24 hour notice, and you are allowed to under under the same notice rule "to carry out a repair or replacement or do work in the rental unit", where cleaning the place is doing work in the unit.