Do Saga and Martin speak Danish, Swedish or both?

They both speak their native language. Saga speaks Swedish and Martin Danish.

I have no idea about the other characters as I haven't seen anything of the show myself, except for trailers, but they are most likely speaking their native language. So, whoever you can identify as a Swede would most certainly be speaking Swedish, and all the Danes would most likely be speaking Danish. Most Swedes have a bit of a hard time understanding Danish, though, so don't be surprised if they start speaking English all of a sudden.

When Martin speaks to a Swede, he articulates every syllable and softens the glottal stop characteristic of Danish (stød), moving his speech toward something you could call a toneless Norwegian, thus much easier for a Swede or Norwegian to understand. When he speaks to another Dane, it's regular conversational Danish. The Swedes simply speak Swedish.

Swedish and Danish (and Norwegian) are mutually intelligible. You can compare them to Serbian and Croatian. The danes in the series speak danish and the swedes speak Swedish.

I watched the first two seasons. I enjoyed the reality that they spoke three languages just like many in those countries would. The Danes speak Danish and the Swedes speak Swedish. Also, when they are on the phone to someone in a country other than Denmark or Sweden, they drop to English just as many would in real life. This really added to the show and it came out great.