You shouldn't put numbers in quotes, that makes them text.
=IF(AND(X3<15,X3>7),1,IF(AND(X3<80,X3>0),2,IF(AND(X3<0,X3>-3),3,IF(AND(X3<-3,X3>-3),4,"N"))))
Your last choice doesn't make sense though how can X3 be less than -3 and greater than -3? Also X3<80 isn't in your example of what you're checking for.
You may want to look at VLOOKUP though:
=IFERROR(VLOOKUP(X3,{-7,4;-1,3;0,2;8,1},2,1),"N")