I disagree on the recency being an issue - they're over three years old. I know that a USDA loan only has a twelve month requirement, and you're well past that. You *might* pre-qualify, but will most likely have the condition of paying off those collections, or at least evidencing a payment plan with the creditor, the monthly of which will be factored into your DTIR. Your car note is already pretty huge, so with the addition of the collection payments, your ratio might kick you out of the price range you're looking for.
I would suggest working to settle those collections ASAP. Since they won't PFD, and assuming you can't PIF, offer to settle for 25-50% and then pay it off immediately. Try to negotiate the wording from "Settled" to something more favorable, like "Settled in Full", or "Pays as agreed". Do not enter into a payment plan with a CA; just pay what you can get them to agree to in one lump sum and get it done. That way they'll come back closed with $0.00 balances when you try again for a mortgage. They'll still be there until they fall off, but the underwriter will be more forgiving knowing that those collections pose no threat to the mortgage.
