How can I get an ID if my visa is expired and I lost my passport?

You have to contact your consul and ask for a new passport. After you get a passport, you can marry; the city clerk will not ask you for a proof of your legal immigration status. To obtain a green card after the marriage to a U.S. citizen, you would need proof of legal entry into the U.S., in other words, a copy of your H1B visa and Form I-94. The U.S. Government has these documents, and you can obtain them under the Freedom of Information Act. You can try doing it yourself; but, since retaining an attorney to handle your legalization process would be a good idea anyway (considering your immigration violations and prior marriage), your attorney will request copies of your entry records. Considering that obtaining the records takes very long time (9 months to a year is not uncommon), you might want to start the process as soon as possible, without waiting for a passport and a marriage certificate.

You may want to start with your consulate, and request a new passport to start. You will also want to confirm what identity documents are required in the county you wish to marry in. And you will need a copy of your birth certificate as well.

You can always apply for a San Francisco ID card or just renew your passport.

You should get some help to search for the missing information. You will have to replace those documents.

Contact your Embassy to get a new passport. You will also need to get proof of your lawful entry to the US, using the I-94 card. If that was also lost/stolen with your passport, you will need to either apply for a duplicate or collect secondary evidence proving your lawful entry.