How do I evict a tenant withou a lease in Illinois?

First its not a good idea to piggyback your question on someone else's. This can lead to confusion. You should start a new thread. So I've moved your question to its own thread.

Whether a tenant has a lease or not has little bearing on the eviction process. The main difference is that without a lease they are assumed to be a month to month tenant, so you start by gibing them one month to vacate, unless they are violating some provision of the tenancy agreement (like not paying).

From there the process is the same, to find out the details for your locality, go to your local court and ask. The details vary widely even within a state.