The one I've found to be most similar is this one; http://www.omega-watch-collection.com/omega-watches/#omega-285-arabic-numerals-jpg Haven't seen too many Omegas with arabic numerals.
Quite genuine. This watch would have been offered with many different dials. Yours is indeed fairly uncommon but not considered rare. The information to identify your watch can be found inside the case. The model number should be stamped inside the case back and the serial number will be found on the movement itself. Take it to a watchmaker to open and get some good clear photos of the insides then post them here for further help/information.
My granpa lived in Norway all his life. Not sure if he bought it overseas though. I'll try to get it opened at a jeweller when I get the chance. It needs a fair bit of polishing I think. Is there anything in particular I need to be careful about?
I'm sure the British Isles aren't the only place Arabic dials ended up, but they do seem to be more common there as a general guideline. You need to be careful about polishing it. It looks fine to me; there are no large gashes in it that I can see. It's a vintage watch and it shouldn't look like a brand new one with mirror shine lugs. I'd highly recommend you do not polish it.
Quite common with Arabic numerals for Norwegian ones too, and from what I've noticed other parts of the Norwic countries too. To the OP, there are just a few places in Norway you should take this watch, and any jeweller is not one of them. I can recommend some watchmakers in Oslo. Sjekk ut vintage delen av tidssonen.no også
Do not polish the watch and make no attempt at "cleaning" the dial. Leave the watch as is except for a servicing of the movement. A vintage watch's value both monetarily and sentimentally is in its originality, bumps, bruises, aging and all.
Polishing a vintage watch has a huge negative effect on the monetary and aesthetic value. Think very carefully before having it polished. A good clean of the case and movement service would be the best way forward.
What about the watchband, is it of significance? It's not exactly my preferred style, and I don't think it's an omega watchband.
Wasn't able to have a look at the watch until now, since it was in Europe and I'm in Australia. Got the back off to have a look at the movement. It doesn't run, suspecting it might be the main spring. Is the gasket supposed to be greasy like that or is it a poor gasket or just deteriorated?
Yup, all looks correct. Nice watch and fun to have all the numbers. It'll be much better if you got rid of the stretchy bracelet and put it on a nice leather band as the metal bands typically chew away at the points of contact to the watch.
It appears to be simply deteriorated. As mentioned above, a good case cleaning and movement servicing will solve that as new gaskets are (typically) a factored expense from a trusted / vetted watchmaker. Really nice watch and the movement looks super clean!