Can I file for my sister or should her son be the one to petition her?

It is much quicker to have her US citizen son petition for her. However, if your sister overstayed her visit by 1 year or more, the earliest that she can return to the US is 10 years after her last departure unless she is eligible for a waiver of the 10-year bar. To qualify for the waiver, she must prove extreme hardship to a spouse or parent(s) who is a lawful resident or citizen of the US. The petition is filed on form I-130 and the waiver application is filed on form I-601. She should not file the waiver application until instructed to do so by the US consulate after her visa interview.

Will be much after if her son files petition.

The son should file. Is the mother subject to the 10-year bar?

Generally, it would be best for her 21 year old U.S. citizen son to petition for her. But she may have a problem with the overstay, i.e. she may need a provisional waiver if she overstayed more than 180 days. I wouldn't advise either you or her son filing without a lawyer because her case sounds too complicated for a pro se filer.

Her son should file for her. You can be a co-sponsor if the son does not have enough income, but he should be the petitioner for his mom.

If your sister overstayed less than one year, it should not affect her eligibility for an immigrant visa. If she overstayed 1 year or longer, she is inadmissible for 10 years, and a petition you or your nephew would file now would be denied; you should wait until 10 years will pass since she left the U.S. On your petition, your sister will have to wait for a visa about 12 years (17 years if she is a Mexican citizen, 24 years if she is a citizen of the Philippines). On her son's petition, the process will take a year to a year-and-a-half.

It would be so much quicker if the petition is filed by the son. The petition will be filed under Immediate Relative category, which means a visa number is immediately available for the beneficiary. It will take about 6-9 months for the immigrant petition to be adjudicated. Once approved, it will be sent to the National Visa Center for processing of immigrant visa application. Assuming your sister is not subject to any other inadmissibility issues, she may re-enter the United States after the 10-year unlawful presence bar is up. She has been outside the United States for 8 years, so by the time she applies for immigrant visa, the 10-year bar may already be up or she may just have to wait for a few months only. If for some reasons the son is unable to petition her, you may file a petition for your sister under F4 category, which has a long waiting time depending on your sister's country of birth. Based on the October Visa Bulletin, the wait times range from 12 years to 23 years.