What does “case currently not assigned to process” mean?

It means your case is still pending and an immigration officer has not been assigned to process you case, although it would eventually be assigned and processed. But in the meanwhile, the only thing you can do is to wait and keep checking at regular intervals. Lastly, at some point your case will be assigned and processed. The decision whether an approval or denial will be made and sent to you.

"Case currently not assigned to process" means just that; for whatever reason they have not yet reached your case and they have not transferred it to the district or field office for you to be scheduled for your final interview. There could be a number of reasons why this could happen, including some issue in obtaining the necessary security clearance.

It is not a denial. It means that the case has not been assigned to an adjudicating officer to process yet. Seems strange if your I-485 has been pending for over 24 months. You should definitely do an Infopass apptment or have your attorney do so to inquire regarding this case.

It means that it has not been sent to an officer for adjudication. Adjustment is not faster than immigrant visa processing. Make an Infopass appointment, go down and ask them to please schedule the interview, but first make sure your priority date is current. That is, you have reached the final action date on the Visa Bulletin.

Your case has not yet been assigned to an adjudicator for processing.

Assuming your priority date is current and your I-485 has been pending for longer than the USCIS processing times, you should have your immigration attorney make an inquiry regarding the status of your case. If USCIS customer service is not helpful, you may need to seek congressional help.

This does not indicate a denial. Adjudication of I-485 are often backlogged. Your case is still in the queue to be adjudicated. Given the length of time it has been since you submitted, I would advise you speak with an immigration attorney to make an inquiry with USCIS.

If your priority date is current and your I-485 has been pending longer than the posted processing time for that service center, then we always call the customer service number or send an e-inquiry.

It is not clear how recently you sent in the inquiry, but "case is currently not assigned to process" means that no one has been assigned to review. This could just mean your inquiry has not been assigned to anyone for a response. However, since two years pending for I-485 is a long time, I would have your lawyer call to inquire or seek congressional help.

Your immigration attorney can make an inquiry to the national customer service center to check on that (heck, you can too as the applicant!). I cannot say I have seen that case status before.