Is it all right to sue a landlord?

It would be pretty difficult to make stick. It is, after all, the landlord's property. And I'm sure the lease allows them access to inspect and repair and those sorts of things. But there is also likely to be some Wording to the affect of 'reasonable access' and 'prior notice.' And if they were showing up in your bedroom at 2 in the morning, there might be something to it. Trespass is not likely the charge, but there are other torts that might fit the situation better.

Yes, absolutely! While the landlord may "own" the property, he does not "possess" the property while you are the tenant. Thus, entry upon your property without permission or valid excuse is (legally) trespass, and probably also a violation of the lease agreement (if you have one). In many cases you can obtain a rent abatement for every day on which you were denied the value of your property rights (not to mention restitution for any damages caused during the uninvited visit), and you may obtain an injunction to prevent further violations to your privacy.