Well it sounds like you avoided foreclosure, even if you went 120 days late on it it's still not considered a foreclosure unless an actual foreclosure happened, so that is good because a foreclosure is a 3-year wait for FHA & USDA financing. The late late payments on credit cards & installment loans wouldn't be an issue from back in 2008, however if the judgment was within 3 years of your application then it'd disqualify you from our FHA loan program that goes down to a 600 score (we have much easier guidelines once you reach 640, including being eligible for USDA financing). It's relatively easy to get your scores up to a 600 level, but unless you have at least 3 to 5 trade lines reporting on time payments each month... the ascent up from the 600 level is a slow one. Regarding your unpaid collection & charge-off accounts, I wouldn't pay them off unless an underwriter requires you to because as you've been told paying them off could have some negative impact to your scores. As far as your chances of your credit being OK at this point are roughly 75%... if you had 640 scores that would open up more lenders, as well as make lenders FHA underwriting guidelines go easier on you, and the chance of your credit being OK in that situation would increase quite a bit, I'd put it at around 95%. Plus having a 640 score will open up a lot of USDA lenders as choices (at a 640 score USDA allows lenders to waive certain credit issues, including unpaid collection/charge-off accounts), which is a better program than FHA in my opinion.
Where did you get your credit scores from? I wonder, as pretty much all websites where consumers can check their own scores at are giving out incorrect scores, "FAKO" scores we call them since they are a fake FICO score. There are different scoring models that various lenders use (mortgage lenders, auto loan lenders, credit card lenders, etc.) and the ones that mortgage lenders use actually cannot be obtained by consumers at this point (other than if a creditor checks your credit and provides them to you). So unless you got your scores from a mortgage lender, you may be unpleasantly surprised that your real scores may not be as high.