You certainly are entitled to pursue support from him. How you can best go about it will depend on a few things:
First, is support enforcement being handled by the District Attorney's office, or not? In most cases, the Child Support Enforcement Division of the Department of Justice handles collection of child support. If his driver's license is suspended for non-payment, then that strongly implies that they're aware of this case already. If they're not collecting, that implies in turn that he doesn't have any money to pay. He's legally obligated to pay, and as long as he doesn't, arrears will continue to accrue; but if he has no money, then he has no money you can take.
That's the next question: what assets, if any, might he have? If he has a job, then you can garnish his wages; bank accounts can also be garnished. You can also place liens on any real property or other substantial assets that he owns. You need details on these assets to garnish, but he can be summoned for a judgment debtor exam before the court, to discover these details. Again, the DA normally conducts these, but you can also hire private counsel to try to speed the process along.
In general, you will not be able to pursue his new spouse for support. Oregon is not a 'community property' state, where all property owned by each spouse is assumed to be equally the property of the other. His new wife is not responsible for his support obligation. However, any property that they acquire jointly during the marriage - a house, for example - might be subject to seizure or garnishment.
Costs vary; most attorneys would want a retainer of at least a couple thousand dollars before taking on a case. But you may be able to recover these costs from the father as well - assuming again, of course, that he has any money to pay. You can call the Oregon State Bar for a free referral at 503-684-3763.