Rectangular electrical box doesn't fit. How can I install receptacle?
Is this already an existing box (just with damaged threads) if so then you can use some 1" #10 wood screws instead of the mounting screws that come with the outlet, this I a common problem I run in to on service calls (I am a apprentice electrician).

The other thing is that box you purchased is not a typical wall box instead you may want to try an 1104 box like this 

And if you are mounting it to the drywall instead of the stud (common when drywall is already up) use some f-clips to support it it is hard to describe the installation in text so try this simple youtube video or you can use a rework box such as this as they are much easier to use but a bit more expensive (still under $10) 

I hope this helps