To answer your specific question, the type of OBD reader you're probably thinking of are OBD-II readers that can only be used with the OBD-II diagnostic connector ports located in the interior of later 1990's cars (1996-on), not the underhood OBD (OBD-I) diagnostic connector in your car. Even if they could be used, your diagnostic connector port would need to be functional. As others mention, you perhaps need to be a bit more precise describing not being able to get any codes.

The code retrieval and reset procedure as well as other diagnostic procedures you are able to perform at the connector are described here in the brickboard FAQ
Engine: OBD Codes (700-900 FAQ)

If the red LED won't light at all when you depress the button with the ignition switched on (KP-II) and the pigtail in either socket 2 (fuel side) or 6 (ignition side) then you have a basic electrical problem likely at the diagnostic socket.

If it glows faintly without having to depress the button (possibly only noticed in the dark) then there may be a ground problem on the ECU circuit board. This was more common with a few of the early LH 2.4 ECUs that also had failing fuel pump control, not the later ones like yours. With a bad ECU causing the LED to glow, the OBD socket was generally still capable of being used.

For further information, you may want to check out this older thread over on Turbobricks, possibly the same problem as yours
Volvo 240 OBD not working (Turbobricks)
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Dave -still with 940's, prev 740/240/140/120 You'd think I'd have learned by now