YOUR ADVICE WILL BE APPRECIATED
I informed my landlord a month be the expiration of my rent that I am moving out of his house, now the rent is expired and am yet to get a good apartment, my Land lord said she’s only given me a week, but am so sure that even if I get a house within a week, can I renovate it within a week, pls I want to know my right as an outgoing tenant, how many weeks or month am I entitle to as an outgoing tenant, pls lawyer in the house help me.

In the real sense you are not entitled to any free weeks or months. Only if you have a good relationship with your landlord.

You told him you won't be renewing your tenancy at expiration which only implies there would be a close of contract at expiration. However, you are still in possession which means a breach of your contract(though orally).

You would be expected to pay a 'mesne rent' to the landlord which means an amount payable during the period you owe him over. The rent shall be pro-rated per month.

It depends on the nature of your tenancy but the minimum is one week(if you are a tenant at will).
When you spoke to your landlord, did you sign any undertaking? If no: you are entitled to your Notice to quit and Your Notice of owner's intention to recover possesion.
Meanwhile find house sharply