I found this in a second-hand store in Berlin for $100. The bars that attach to the strap are bent and the face has a slight movement to it when winding. I brought it to the Omega store on Madison Avenue in NYC and they said that they could not service it in store because of the age, (1938-1943 I think?), and that it would cost a couple thousand dollars for them to send it to Europe. I posted on reddit r/watches and somebody said that the dial might be radioactive? Anyway, I was hoping somebody could give me some information about the watch and whether it is worth servicing, and where. Thanks!
The dial is almost surely to have been repainted. The guys that really know about these would need to see the insides, movement and inside of caseback before detailed information can be provided.
From what I can see, the dial is original but the radium has been removed from the numerals. The 'Cathedral' hands still have some radium lume intact. I don't think this is from 1938/1940, probably 20 years earlier than that. Any more information will require you to provide decent well lit hi-res photos of the: Dial (front on, no angled shots). Inside caseback. Movement, including diameter in millimetres. Trench watches are growing in popularity but to the uninitiated they can be risky as they don't have the shock protection of modern mechanical movements and parts can be very hard to source.
Look for a slot or lip built into the caseback to assist you in carefully levering the cases snapback off. If you don't see one and are not sure which tool you must use, I'd suggest this one! Don't handle the movement with bare hands, just get your pictures and get out! By the way, if there are no cracks in your dial face, I think you got your money's worth. Too bad about the case wear.
I think it is a caliber 26,5, but I cannot see the first digit of the serial number, so cannot give any date. Cannot see any markings on the case back. Is there any? I agree with Jim: likely the original radium dial with the radium been removed. But there is still radium on the hands so do not play with them! This caliber is not hard to service. Parts are getting harder to find, but you can still find several of them and buy a donor if necessary.
Why are some Omega's, like this one, valued so little? Because they are so old or because they were made as inexpensive watches?
The fact there is no script or logo on the inside of the back is weird. It would indicate that the case is not Swiss made and maybe that the watch has Ben recased. Moreover the case seems in rather poor condition.