What I've done dozens of times with these DIY build additions is first really look it all over from the roof down and see if it's even worth fixing.
Reality sucks, but it makes no since to waste time and money on something that's just going to fail again.
Often times I'd find the roof had been leaking for years, undersized rafters, not enough roof slope, tied into the house wrong.
If I was stuck having to just repair what you have there, first thing I would do is remove all those undersized floor joist, and anything else inside the crawl space, then see if there's proper footings and enough of them under those outside walls.
Check for rotted or insect eaten wood at the bottom of the walls.
Check for level and flat as best I could to see if the colums had sunk or were failing.
If all that looked good then I would be cutting a 2 X 10 pressure treated to length to fit along that long wall attached to the inside of the rim joist or beam if that's what you have instead.
What I do at first is insert three 3" long decking screws into the board before installing 2 on the ends one in the middle.
I first screw in the middle screw, then cheaking for level I insert the end screws.
(there's a reason for just tacking this up like I suggest, you will soon see)
Do the same for the end walls, and last the one along the house wall making sure all the tops of the boards are even in the corners.
Now I lay out for my floor joist every 16" O/C.
Once it's laid out you'll now know where you can insert LedgerLok screws without them being in the way of the joist hangers.
At a minimum I'd be using 2 X 8 PT floor joist.
Note; I use all PT for the joist because your so close to grade, I'd use 2 X 10's for the rim joist because it's stronger and will help keep those outside walls from sagging.
I'd be using Advantech, not plywood for the subfloor, any nails or screws used need to be ACQ approved.
8D, ACQ approved ring shanks work great.
Advantech comes with the nailing pattern printed right on the panels, do not skimp on nails!
Make sure to apply constrution adhesive to the tops of the joist for a far stronger and less squecks floor.
Never have the narrow butt seams line up when laying the subfloor, they need to be offset by at least one joist bay.
You never want to end up with a really short piece on the end of a run, if it ends up being something like 16" as an example, cut off 16" off the first piece so the end piece will now be 32".
(You want to make sure all the 2 X 10's you use are as straight as possible)
Make sure to check the joist for crown and install crown side up.
Once the joist are in place add blocking down the middle.