First of all, Eviction and Termination or Non Renewal of a Month to Month Tenancy are two completely separate things.
Having your month to month lease terminated by the landlord is not an eviction.
An eviction is a lawsuit where you sue the tenant for possession of the rental unit because they refuse to pay and/or refuse to leave and/or are violating some other term or condition of the lease.
Are you evicting the tenant for non-payment of rent? In this case, you'd normally serve the tenant a "pay or quit" notice (it's called different things in different states, but that's the gist of it: Pay us everything you owe before this notice expires, or move out, or we're going to evict you.)
Here in Florida, once such as notice has been posted, you MUST accept payment in full prior to expiration of the notice. You don't have to accept a partial payment. IF you do accept a partial payment, the eviction notice becomes null and void (but you could take the partial payment and serve a new notice for the new amount owed and start over). Sometimes this is a tough call: Do you take the money, or do you preserve your right to move forward with the eviction and get it over with?
Or are you simply terminating their month to month tenancy? If this is the case, then you should expect to collect the rent as stated in the lease through the time the tenancy expires, which you stated is March 31st. Assuming you served a legally sufficient notice, if the tenant stays beyond March 31st, you could then evict them for holding over, commonly referred to as a holdover eviction.
But this is complicated by the fact that I think you are saying you already accepted payment for April, May, June, and July as well? On this point, you need to talk to your attorney. If I were the tenant, I'd argue you already extended my tenancy through July 31st, and you can't have it both ways. And the judge might very well agree.