Every dog owner is obligated to keep his or her dog in his or her own yard, and the owner is liable for any harm caused by the dog if it roams. If the facts are as you describe, you probably have no defense to the charges.
(THESE COMMENTS ARE NOT LEGAL ADVICE. They are provided for informational purposes only. Actual legal advice can only be provided after consultation by an attorney licensed in your jurisdiction. Answering this question does not create an attorney-client relationship or otherwise require further consultation.)
"my dog got out of my backyard...I woke up the [to?] a bloody dog and the police."
Which is to say, your dog was not under your control or even on your property when it injured another dog IN its house and a person also in that other house. Unless Albany, Oregon has no "leash law" at all AND a "one free bite" exemption, you are almost certainly liable for the damages your dog caused during its excursion. That you now face "dog at large" and "public nuisance" charges indicates it has both a leash law and strict liability for bites.
You state you "paid their vet bills." What about the injuries to the person trying to break up the fight? As the fight occurred in a home, were there property damages? In other words, what other harm did your dog cause?
Your primary question is whether you should "fight the charges any defense?" I suggest you contact an attorney versed in dog bite cases to give you more specific guidance. Based upon the information you have given, you will likely need legal counsel.
Unless there are facts you didn't post, I don't think you have any defense. "Their version" is irrelevant because your dog was loose, caused damage, and you are liable for that damage. The Oregon State Bar Association, http://www.osbar.org/, has an animal law committee; they may be able to advise you further.
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