What you should do is controlled by the written terms of your lease agreement and the landlord-tenant law of Ohio. You need a real estate attorney who practices Ohio landlord-tenant law to help you. If you do not act propmtly to get help, your landlord may evict you.
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It is impossible to say what is a "proper legal notice" without having seen the notice. I will say that these types of notices need to comply with Ohio Revised Code Section 1923.04 (http://codes.ohio.gov/orc/1923.04). Make note of the language in section (A) that must appear in the notice. Generally, if a landlord was seeking to evict for non-payment of rent, you would see a 3-day "pay or quit" statement in the notice which would require you to pay up or get out within 3 days or they could start the formal eviction process.
If what you quoted above was all the language contained in the notice, and your lease expires in August anyway, it sounds to me like they are letting you know that they do not intend to renew your lease or permit you to stay beyond lease expiration on a month to month basis. Of course I cannot know that for sure without getting clarification from the landlord, but I would suggest that you go ahead and make alternate living arrangements effective the day your lease ends (July 31st?), and if they didn't accept your July rent I imagine they will swipe your security deposit to cover that last month.
When in doubt, it is always good advice to consult with a local landlord/tenant attorney who can review your lease in person and perhaps have some success in contacting the landlord. I hope this was helpful, and best of luck to you.
I am licensed in the State of Ohio, posting a response to your question or issue does not create an attorney-client relationship and I AM NOT providing you legal advice. You should speak with an attorney who is licensed in your state to whom you have provided all the facts, before you take steps that may impact your legal rights--or rights to recovery of damages.