You need to talk to a priest. If his second marriage was not in the Catholic Church, it was not valid anyway. You will never know the answers to these questions until you talk to a priest. …]
This is the best possible advice for you. Chances are that everything can be resolved and both of you can be fully reconciled with the Church’s teaching on marriage, but only a priest can guide you properly through what needs to be done.
If your husband’s first marriage was annulled before his second, and the second was a marriage in the church, then that second marriage will need to be reviewed to see if it might also be able to be annulled. If these conditions weren’t met, the second marriage likely wasn’t valid anyway and can probably be recognized as invalid quite easily.
Assuming that the nullity of his previous marriages can be established, and assuming that you don’t have any previous marriages or other impediments of your own that need to be resolved first, your marriage can then be convalidated and recognized by the Church. Again, your priest can guide you through all of this.
As it stands now, you and your husband are not actually married in the eyes of the church…so both should refrain from receiving the Sacraments. If, God forbid, your husband found himself needing to receive the last rites, he would need to renounce his sin. That’s not renouncing YOU, but could perhaps mean he needs to renounce his presumptive invalid marriage to you (since, in the eyes of the church, he is married to another).
But definitely start getting everything straightened out well before either of you needs the last rites! I work with the RCIA program in my parish (for people, like yourself, considering becoming Catholic) and we deal with these kinds of issues all the time. Be patient, follow the guidance of your priest, and chances are that everything can be resolved and ‘normalized’ in the eyes of the church with regard to your marriage.
God bless!
Take it one step at a time and go see the priest ASAP.