Annoying check engine light & minor problem won't pass emissions test

Any chance you misunderstood what they said and took the word “several” to mean “seven”.
If your car had 7 O2 sensors, which it does not, you would not likely be getting off the hook for a total replacement cost of 750 dollars.

Other than agreeing that you should get a parts house to scan the car and post any codes, one issue with something like this is the fact this has gone on for several years. What may have originally been a minor 5 minute fix (vacuum leak for example) may have snowballed and created a number of problems.

And emissions can be affected whether any driveability problem is noticed or not.