How can I do offset nulling for this opamp circuit?
You could add a pot as shown. The LM324 is not a good op-amp to use for mV DC signals- offset can be as much as +/-20mV and this will only adjust for +/-5mV offset (you have observed 0.5mV). 







simulate this circuit &ndash; Schematic created using CircuitLab

If you don't like having to come up with +/- supplies (or having it drift around by maybe 5-10mV/°C at the output), use a better single-supply op-amp. 

Edit: Since you are using a thermocouple, and assuming it is floating, you can (and should) offset the input by adding a voltage divider to a reference on the (-) side of the thermocouple. Otherwise you'll never be able to measure below the temperature of the instrument terminal block. It's possible to combine the voltage divider with a temperature sensitive element to both offset and cold-junction compensate the input but that's way beyond the scope of this question.