Do you have a phone designed for use in Slovenia, i.e. not one that you brought from the US or a third country? If so, try connecting that phone directly to the wall jack (OBi not in the path). If caller ID still doesn't show up, either you don't have caller ID service, or you have an issue that you will need to resolve with your landline carrier. If your landline is sending caller ID, we can try changing some settings to get the OBi to read it.
If you can't get landline caller ID to work, there are several other options:
1. Have the autoattendant answer all calls, either immediately or after a delay. Of course, you would use a strong PIN to prevent unauthorized use.
2. Use a service such as Localphone. Once set up, you dial a Ljubljana number and it rings your contact in the US. Of course, it's not free -- most US destinations are $0.005/min. You get a five minute free trial at signup. This method has nothing to do with the OBi.
3. You can set up Localphone to call your OBi for free, which can then send your calls via Google Voice. You'll need to pay €5 to start your Localphone account, but there will be no per-call cost (except cellular minutes).
4. If oubound calls on your cell plan are expensive, e.g. a prepaid card at €0.18/min., you can set up the OBi to do callback. You call it from your mobile, it doesn't answer right away, you hang up and it calls you back. You can then dial your destination number through the autoattendant. The call to your mobile is of course not free, but will be less than making an outbound call. IMO, good choices for a VoIP service for the callback leg include GV (simplest, $0.15/min.), Anveo (high quality, $0.091), CallWithUs (decent, $0.0695) and Voxbeam (good but entails some hassle, $0.0579)