You can sue the roofers even though they are not licensed. However, because they have no license, they probably do not have the right to sue you pursuant to RCW 18.27.080. A link to the statute is below.
I hope this helps.
Ball Janik LLP
Disclaimer: This answer does not create an attorney-client relationship and is for informational purposes only. It is not, nor is it intended to be, legal advice. You should consult an attorney for legal advice addressed to your individual situation.
Remember that a lawsuit can be expensive and if you didn't enter in a written contract with them that included a discussion of the payment of attorneys fees, you could conceivably win the lawsuit but have to pay the legal costs. That could mean that you end up spending more on attorneys fees than it would cost to fix the roof.
I'd suggest getting a couple of written estimates documenting what's wrong with the roof and how much it would cost to repair it. Then, either by yourself, or with the help of an attorney, send a demand letter to the roofer for the amount needed to fix the roof. If that doesn't work consider taking them to small claims court (for the amount needed to fix the roof). In smalls claims court you typically would represent yourself, but an attorney could help you prepare your case ahead of time if you desired. You could also hire an attorney to help you sue the roofers in district court. Your attorney would be able to discuss the facts of the case with you and advise you whether you will have an opportunity to recoup attorneys fees.
If you've discovered that the roofers have violated state or local rules regarding licensing or permitting you also have the option of reporting them to the appropriate licensing body. The roofers might be more willing to repair or pay to repair the roof when they learn you plan to report their shoddy unlicensed work.
I hope that's helpful.
Providing this general response does not create an attorney client relationship.