I think your first problem is coming from this assignment:
strTemp = employeeNames[maxIndex] = employeeNames[i];
try changing that line of code to this:
strTemp = employeeNames[maxIndex];
The assignment you're doing assigns the value of employeeNames[i] to both employeeNames[maxIndex] and strTemp. You need strTemp to contain the value at employeeNames[maxIndex], but that's being overwritten before you have a chance to store it. That is why your array isn't changing at all.
Secondly, the check in your nested for loop should look like this:
if (employeeInformation[j][GROSS_PAY] > employeeInformation[maxIndex][GROSS_PAY])
and the line inside of the if statement should look like this:
maxGross = employeeInformation[j][GROSS_PAY];
note the j (you're checking index i).