You "can" sue anyone for anything. That just means you file a claim in court and pay the necessary fee. It doesn't mean you have the necessary claim or evidence to win anything. You have the burden of proving the landlord violated your rights or damaged your property. The fact that your entire story could be summed up in 25 words or less would seem to indicate it's a troll fail.
However, as an academic exercise:
1. a tenant generally owns the exclusive right to enter their private home at any time. The landlord owns the building; not the right to enter.
In the USA and many other "common law countries:", the landlord cannot legally enter without tenant's consent, except in states that have passed laws allowing otherwise, including allowing a tenant to agree to allow it in the written lease. Most states have laws granting a landlord a LIMITED privilege to enter your home by giving prior reasonable notice (typically 24 hours), except for emergencies.
2. A tenant could sue for trespass (damages to be determined), the LL would offer various defenses, such as having some "right to enter", if they can prove that. In some states you could automatically get a restraining order by telling the court your landlord entered without your consent. In some states the tenant could have the landlord arrested for trespassing, if not also malicious destruction of the tenant's property. Again, the landlord would have various possible defenses.
2. A landlord (or anyone else) can be held liable for intentional or negligent damage to a tenant's private property, regardless of where or when it occurs. The tenant has to prove that the damage was "caused" by the landlord, and would not have otherwise occurred, among other things. The landlord would have various defenses.
3. You can sue for refund of your rent, when the landlord has violated the law or the terms of your lease. As mentioned above, you can sue for a restraining order. If you can prove the landlord was intentionally wrong, you may also request punitive damages ("a million dollars") to make a dramatic example for others (not to mention making it more appealing to attorneys to give you counsel).
4. People spouting pseudo-law from Nolo tenant-rights sources would do us all a favor by admitting they have no idea what they're talking about, or at least citing the source for those who don't recognize the recurring misunderstanding of the law.
Your local laws and lease depend upon circumstances we can't begin to guess, so it's up to you to find someone locally licensed to practice law and to give you actual legal advice for your situation.