Can I petition my stepfather even though he and my mother are not married?

NO, you cannot. Your mother and stepfather need to have been married prior to your 18th birthday in order for you to be able to petition for him.

No, that is not possible.

If your stepfather and your mother are not married, he is, legally, is not your stepfather. Moreover, the immigration law requires that the stepfather/stepchild relationship be formed before the stepchild reached 18 years of age. If you are 21 now (and you cannot petition for your parent, biological or step, until you reach 21), it appears that the law will not recognize the man who marries your mother now as your stepfather for whom you could file an immigrant petition. Your attorney could make some creative arguments in support of your ability to be your stepfather's immigration petitioner, but it is difficult to predict whether these arguments will be accepted by the court. In any case, without your mother's marriage to your stepfather, you cannot do anything for him.

If they were not married prior to your 18th birthday, no.

If you can establish an ongoing and valid step-parent/step-child relationship that satisfies immigration laws you may be able to do so.

You can petition for your step-father if you are at least 21 years of age and he marries your mother before you turn 18 years old.