It should be easy to determine something that will work. Most 14 pin dip op-amps use the standard pinout for a quad device. As a reference, use the datasheet for an LM348. http://www.st.com/content/ccc/resource/technical/document/datasheet/50/11/0f/1c/28/6f/4b/ea/CD00000462.pdf/files/CD00000462.pdf/jcr:content/translations/en.CD00000462.pdf
Start with that assumption and trace the PCB to see if that makes sense. On the quad device pin 4 is V+ and 11 is V-. That should be easy to check. Next look at the 4 corner pins 1,7,8 and 14. These are outputs. Another trick is to power the unit up and see if all of the + and - inputs pins (e.g. pins 2 and 3) are at the same voltage. This assumes that the section being tested is functioning correctly and is being used as an amplifier (as it most likely is). You can also check the DC voltage present on the 4 output pins. If a bipolar supply is used (e.g. +/-15 Volts), you would expect all of the outputs to sit at 0 volts. If a single supply is used, then look for 1/2 of the supply voltage.
Once you have some confidence that this is the correct pinout, you can choose from a large array of op-amps that will work in the circuit. If the circuit is powered by a single supply (e.g. +12 Volts), try to sub in devices rated for single supply operation. However, most amps will work in single supply mode with no problem. The TL074 is a very common quad device that would probably work in the circuit if you determine that it is indeed a quad.
The board looks like it was hand etched, so use caution when unsoldering the old part. I would put a good gold plated screw machine 14 pin socket in place to avoid any further need to solder.