It will depend upon a lot of elements. It depends upon how quickly the Landlord processes the papers against you and contacts the Sheriff to evict you. It also depends upon how busy the Sheriff is at the time with other evictions and matters. It also depends upon whether you bring on an Order to Show Cause to stop the eviction for some legal reason and how long it takes to get the Court to make a decision. All of these things vary from one jurisdiction to another. So its impossible to tell you exactly how long it will take.
Usually, however, you get approximately 60 days from being sued to leave. Make sure you don't let it get so far that the Sheriff has to actually evict you, however, because that can result in actually getting all your belongings placed on the side of the street and anyone can come along and take whatever they want if you or someone else is not there to safeguard them.
You may want to try to get some help from Catholic Charities or Social Services with rent assistance.
it depends, could be months or more. Once the sheriff serves you with the complaint and summons and you decide not to contest it (you should however retain counsel to assert your defenses and there are ways to slow down the process, ie file a jury demand) the judge will then order you out in anywhere from 7-28 days depending on a number of factors. Then the sheriff will evict you when your time is up it also depends on the sheriff's schedule it could be a few weeks or months after that. in cook county, even after the time has elapsed, the sheriff takes a number of months to throw them out
There's alot of variability.
On the day of court, a "stay" day will be set. This can vary between 7 days (if you don't show up) to a couple of months (rarely though). If you don't contest that you owe and just need some extra time to move, it is a good idea to see if your landlord's attorney would be willing to give you some extra time in an agreed judgment (as opposed to going to trial). A landlord doesn't have to, but most reasonable ones will. If you have special circumstances (small children, a disability) the judge might be willing to give you more time to move, but it's rare to get more then 30 days or so from the day of judgment.
Technically, you have until midnight on the stay day to voluntarily get out. If you don't, the landlord can place the order with the Sheriff who can come anytime to forcibly remove you, generally you (and anyone else living there) will be escorted from the property, all your possessions will be thrown on the lawn or sidewalk, and the locks will be changed. This is best avoided.
In practice, how soon after the stay date ends the sheriff comes out depends on many things; I've seen them go in a couple days or a couple months (Cook Co. is especially slow), but the whole time until they do, you have to live with the uncertainty and the fact that you could come home and find your things in the street if you don't vacate.