The answer varies from county to county. The rules of procedure also provide a couple of different provisions that could provide the relief that you are seeking. As a result, the answer is complicated and requires specific legal advise which can only be given by an attorney after a thorough review of your situation, fact pattern, and court orders.
The first question is which judgment are you referring? There is a "judgment" entered based upon pleadings that start the redemption period after which a sale can occur. There is also a "judgment" that is entered after the sale, which approves the Sheriff's Sale and, per statute, provides 30 days in which to vacate the property. After those 30 days, the Sheriff can evict anyone on the property. The burden and basis for vacating those orders would tend to differ.
There is also the question of language in the order entered. It may or may not be stated to be an appealable order. As a result, a different section of the Illinois Code of Civil Procedure would control any motion filed. The date of the order can be important as the passage of 30 days may impact which section of the Civil Procedure controls.
Any motion would need to allege the basis for your belief the order should be vacated. This should be based in law and fact. While the different counties vary on the issue of "due diligence" and its application to any motion to vacate, you may wish to show what actions were taken prior to the entry of the order in question. You would need to get the matter placed on the court's call (before the Judge that entered the order). This would be done through the Clerk of the Court. Once again, each county has their own process for noticing matters for court. Notice of the presentation of the motion prior to your appearing in court as well as a copy of the Motion would need to be provided to all interested parties. This would include the attorneys for the Plaintiff. There are specific timing and proof of services rules for the transmittal of notices.
Since you would be seeking a rather extraordinary remedy - the undoing of a court order, such actions should not be undertaken lightly. There may be grounds for your action, but the pleadings should clearly and concisely detail any such facts and/or law. There are substantial procedural rules and issues that also apply. Any motion would need to address those matters, too. As such, it is recommended that you immediately contact a local attorney experienced in foreclosure to seek, at the very least, legal advise, if not representation. Should you not know of any such attorney, most counties have Bar Associations that have a Lawyer Referral Program. You can then obtain a name(s) and research the attorney(s) on the internet prior to setting an appointment.