1. Because this is a month to month agreement, ultimately the landlord has the right to increase rents, change the terms, or even seek a termination of lease. So long as enough notice is given, and I would also suggest that the terms be in writing, then the landlord can go ahead and pursue any of those options. For example the landlord may choose to double the rent starting next rent period and if the tenant fails to agree then seek removal via eviction.
2. Because nothing is in writing it falls upon the landlord to prove terms. Since the utilities are not discussed, even if more of them are used up, unless it can be shown that the tenant agreed to pay, then losses are on the landlord.
3. Now, if you simply want them to leave then you must give them notice to quit. If they are failing to pay rent, and you live in a regular property, giving them 5 days is sufficient. If they are timely with rents you must give 60 days in writing as Delaware requires a long period of time where the tenant is not shown to be at fault. Because you are arguing that the breach took place based on unauthorized people on premises, then that is a 7 day notice rather than 60 days. You can use these forms below as templates to get started:
PS. My apologies on the short delay, it took a bit to write this up.