Don't forget you don't magically get an ATPL at 1500 hours, you have to pass the LST in the Sim as well.
Your EASA theory exams are worth nothing in the US but your licence and logbook hours are. Look at Part 61 to see what you need.
Each Certificate and Rating has a single theory exam which can usually be passed with a few days study.
If you don't have 1500 hours you'll need a CPL/IR which means 3 exams (Private, instrument, commercial) although you could get a 61.75 piggyback PPL.
You will not be permitted to fly for a Part 121 operator (Airline) until you have an ATP, but you may fly for a Part 135 operator (<30 seats)
If you DO have 1500 hours you can go straight to the ATP, using your foreign CPL/IR to qualify. Again that's a single exam and flight test - but here's where it gets tricky: before you can take the ATP written exam you need to attend an ATP-CTP simulator course, which is similar to a MCC course. With an ATP you can fly for a Part 121 operator, but only in the RHS as an FO. This is the same for anyone with less than 1000 hours Part 121 experience.
To have a fighting chance at a job with a major you'll need a Degree.
They won't care about any type ratings you have - they'll put you on whatever fleet they need you on.