Ugh... I hate seeing work like that. Whoever built that should be doing something else.
Your cheapest option is probably to buy a Simpson joist hanger or an L70 (can't really see from the pics which would work best) and install on the outside "stringer" to create a better connection to that ledger. Then, make sure the ledger is well connected to the rim joist.
On the inside stringer maybe you can block between the stringer and rim joist so that a thru-bolt could be installed, allowing the rim joist to pick up the stringer. Hard to see if there's enough overlap there to do it though.
Your wood doesn't look pressure treated and your nails are definitely not galvanized.
Your other option (besides starting over) is to add a couple posts directly under your stringers. You might also want to add an L bracket where the stringers land on the concrete, usually when we pour a landing we'll wet set some brackets for the stringers. These keep the top from sliding down and the bottom from sliding out!