Would they have to leave the country when the visa number becomes available or would they be able to adjust their status here in the US?

They would need to seek a waiver in order to immigrate and they would not be eligible for adjustment of status within the US because they have overstayed unless they are protected under 245i (if the petition was filed prior to April 30, 2001).

You may file I-130's on their behalf, but they will need to determine what their options and consequences will be as a result of their overstays. They may also want to explore what other possible options they may have at this time. You can review the Department of State Visa Bulletin for an idea as to wait time for priority dates.

In order for your sons to be eligible for adjustment of status, you must become a naturalized citizen and petition for them before they turn 21 years of age.

First, you need to understand that, after you will file immigrant petitions for your sons, no less than 8 years will pass before they will receive their visa numbers (if they were born in Philippines, visas will not be available to them for no less than 10 years; if they were born in Mexico - 20 years). If you become a U.S. citizen, and your sons remain unmarried, the waiting time will shorten by about 1 year Second, filing of an immigrant petition does not give them any legal status or a right to remain in the U.S. Third, even though your sons entered the U.S. legally, they are not not in any legal non-immigrant status and, under the law, they cannot receive green cards even after your petitions for them will be approved and their turn to receive immigrant visas will come. If they overstayed 180 days, they are barred from the U.S. for 3 years; if they overstayed 1 year or longer, they are barred for 10 years. It means that they have to go back to their country for 3 (or 10) years before they could use their immigrant visas to come and live in the U.S. You can ask the U.S. Government to waive the bar and permit your sons to enter the U.S. without living in their country for 3 (or 10) years - if you can show that keeping your sons outside the United States would cause you an extreme hardship. For example, if the parent is ill or disabled, and the child is the only person who takes care of the parent, the waiver can be granted. Under the current regulations, even if your petitions for your sons had been already approved, their turn to receive the visas had already come, and your application for a waiver were already granted, your sons would have to return to their country and go to U.S. Consulate for a visa interview. We are waiting for new regulations, but no one knows for sure when the new regulations will be implemented. And, in the years that will pass before your sons will become eligible to receive their visas, the regulations and the law are likely to change more than once. Under the present law, the only situation when your sons might receive green cards without leaving the U.S. (and without waiting quite a few years) is if they get married to U.S. citizens. If you do not expect this to happen, you might file the immigrant petitions for your sons now, and they might want to go back to their country so that, by the time their turn for receiving immigrant visas comes, they would already be outside the U.S. for the number of years prescribed by the law. I realize that this is not what you would like to hear, but this is an honest assessment of the situation you described.