You are correct in saying that after your marriage, you will be able to act as a sponsor to legalize your Irish girlfriend. You can sponsor her as an immediate relative, which means the processing time will be significantly shorter than the other family preference categories. Her period of illegality here will also be waived, an option not available to those using the preference categories.
With regards to her son, if you want to adopt him that’s a whole other issue aside from how you will be able to help him gain legal status. The adoption process can take time and money, and given that the child’s father is still alive he’s going to have to also be involved.
The good news from an immigration standpoint is that once you marry his mother you will also be able to sponsor the boy for legal status without having to formally adopt him.
Immigration law will consider you to be his stepparent, and as such you can sponsor him as an immediate relative as well. A stepparent can extend immigration benefits to a child provided that the marriage creating the relationship took place prior to the child’s 18th birthday.
Once you submit the paperwork for your new wife and stepchild, they will be issued green cards on a conditional basis for two years if the marriage is less than two years old at the time of processing.
The conditional can be removed from the green card after the two period by filing additional paperwork with the U.S. Citizenship and Immigration Service (www.uscis.gov) which shows that the marriage is still intact. (There are other ways of removing the two-year condition if the union is dissolved, but it’s so much easier if the couple are still together.)
The green cards will be considered permanent once the condition is removed, and once your new wife has been a permanent resident in good standing for three years she’ll be able to apply for U.S. citizenship.
Once she receives her citizenship her son will also become automatically naturalized if she completes the process before he turns 18. Because he is only four this should be easy to accomplish, and would save him having to fill out naturalization paperwork at a later time.
All of the above should be completed with the guidance of an immigration attorney, who will also be able to tell you more about the adoption process if that’s what you eventually choose to do.