There are lenders that lend below 620 for FHA, I will go to 600. Below 620 will require some additional compensating factors.
More importantly - Has anyone actually gone over your credit report line by line with you and told you how to improve your score? Collections and judgements (no matter their age) greatly affect your credit score. You also need open and active tradelines with on time payments.
This will not get better over time - you need to take action to get your scores up.
I suggest working with an experienced mortgage professional who understands credit (not just a credit score) and can actually give you a plan to get your score up. Then you will not have to worry about finding a lender who will take your score, you will be able to go to anyone.
Sometimes it can be as easy as updating erroneous information on your report.