wow so no audio out, that's a bummer - so it's basically a 1080p monitor with a built-in tuner What a pain!!
What's your source? You may be able to get away with only using some RCA cables only - although if you are using an antenna to the built-in OTA tuner, you're out of luck there since there is no way to break out the audio - although you could get a component OTA tuner like the IVIEW-3500STBII (I think they are still around for $30 ish) and that could break out HDMI and audio output.
If you have a CATV box, they usually have HDMI or composite output along with the good old RCA L/R outputs so that would work.
Same with a PC, you can view HDMI and get sound via your on-board sound card (you just need 1/8" to RCA adapters) just have to select your audio output as on-board instead of GPU audio.
If you're using something like a roku express, that has HDMI out only, you could also get an HDMI audio extractor, the good ones are around $20+ (stay away from the cheaper ones that can introduce audio lag).
And if you're using any combination of the above, you can probably get away with using an an HDMI audio extractor mated to an HDMI switch box.