The landlord has a right to "reasonable" access to show the unit. "Reasonable" is what you and the landlord can work out between yourselves so you need more of a diplomatic solution than a legal solution. If the landlord gives you short notice of a showing then he shows the unit in the condition it is in. You only need to leave it broom clean when you give it back to him. My last landlord came early to a scheduled showing of my apartment while I was still in the shower. I had him and the prospective tenants wait downstairs a few minutes while I dried and dressed.
Unfortunately, there is no rule or law in Illinois which states when a landlord can or can't enter the property he/she is renting.
The general rule in Illinois is that a landlord may enter with reasonable notice during reasonable times except in case of an emergency unless a local ordinance or the lease agreement specifically states otherwise.
Keep in mind that a renter does have a right to use enjoy the premises and the landlord cannot interfere unreasonably with that right