Your consulate here in the U.S. will renew your passport as long as you are here legally. Get the passport renewed ASAP.
You will be forgiven for any overstay if you marry and adjust through your USC spouse. Make sure the marriage and adjustment is going to work out before you accumulate any overstay time.
Contact the consulate of your home country to renew your passport.
This is not legal advice and no attorney-client relationship has been formed. Then only way to do that would be to to retain my office; if you are interested in that, I can be reached at 703/885-0637.
Get married. Be happy and hire an immigration attorney in your locality to help you settle your immigration issues.
NYC EXPERIENCED IMMIGRATION ATTORNEYS www.myattorneyusa.com; email: email@example.com; Phone: (866) 456-8654; Fax: 212-964-0440; Cell: 212-202-0325. The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter.
If your funds are tight, it is good to know that you are not required to renew your passport in order to apply for, or be granted, an american green card through marriage. I have had many clients get their green cards through marriage even though their passport was expired and they didn't have the money to renew it.
However, as the other immigration attorneys have mentioned, if at all possible, it is a good idea to get your passport renewed through your country's embassy in the USA.