Significance of the song "Should I Stay or Should I Go"?

For me, the scene where Joyce Byers sees the monster for the first time, coming out of the wall in Will's bedroom and runs away from her house, explains it. At that moment she is both devastated by Will's disappearance and terrified of what had just happened in her house. When she gets to the car and manages to start the engine, the radio turns on playing "Should I Stay or Should I Go", and you can see that it kind of calms her down a bit. She is no imminent danger, so hearing the words of the song,

'If I go there will be trouble, An' if I stay it will be double..',

for her might be like deciding between taking off in the car and abandoning Will (or a chance to find him) or staying and facing the unknown alone.

As for Will, In the early episodes, Jonathan has a flashback of listening to this very song with Will. In the background you can hear their parents arguing and yelling, Jonathan acts protective of Will and says they will be alright. He's beeing a good big brother. At the end Will actually says that he likes the song.

So I guess Will is not singing it to contact anyone, he just likes it and feels better taking his mind off the situation and place he found himself in. It might just remind him of home and his family.

I'd say you're reading too much into it. Jonathan liked The Clash (the punk-rock band) and shared the song with Will in one of the times their parents were fighting, as to muffle the sound of the fight and "shield" the young brother from this toxic situation.

Later, when the music starts playing in the house Joyce believes it's Will sending a signal.

In another scene, Will himself sings the song (when trapped in the "Upside Down") probably trying to comfort himself.

I'd say there's no other hidden meaning in the song itself.

I feel like it is as if it has a meaning for will when he's in the upside down he sings it and it means if he leaves there will be trouble (if he leaves the upside down) and if he stays there will be double (if he stays he might die) but then again it's just a theory.