That is a very well-loved watch and a nice heirloom. If you pry off the back, the reference number (basically the model number) will probably be written inside the case-back, and the serial number will be on the. movement, which is probably a cal 30T2, given the 1948 date of purchase. You will also probably see tiny faint hand-engravings inside the case-back from watchmakers who serviced the watch in the past.
The spring-bars should not be protruding outside the lugs like that. Hopefully the lugs are undamaged and someone just installed the wrong type of bars. If you plan to use it occasionally, you will probably want to replace the bracelet (which is not original or made by Omega) with a nice leather strap and get the movement serviced.
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