If I file form I-130 and I-485 simultaneously for my parents can they stay here throughout the process? I’m a LPR. They are here on ESTA for 90 days.

How long have you had your green card? How did you acquire it? How old are you? US citizens have special privileges that allow you to sponsor your parents despite their overstay. Unfortunately green cardholders do not have these privileges. Discuss your case with counsel anywhere in the US via a free consultation. More facts are needed to form an opinion.