You need to file as married filing separately. Head of household would be allowed if you have lived apart more than 6 months, and you pay more than half the cost of keeping your home, and you live with a qualifying person, usually your dependent child. With married filing separately or HOH, you only list your own income, deductions and credits.
Do not try to file jointly.
When you file jointly, you accept full and equal liability for any problems, errors, mistakes, or fraud associated with that return. That means that if there is tax and penalties owed, the IRS can collect from you even if it was not "your fault." Filing jointly means you accept total responsibility for everything on the joint return.
Whatever else is going on in this situation, the last thing you want is to be jointly and equally responsible for whatever shenanigans your ex is up to.
Separately, of course, you should consult with an attorney, likely you need to hire an attorney to push your divorce through from your side and protect your rights. Your attorney can advise you on the bigamy and other issues.
