しょーむない更新失礼しました(T^T) Sorry for the boring update
From my understanding, しょーむない means something along the lines of くだらない and つまらない. Where does it originate from and is it specific to a certain dialect?
There's a couple of similar expressions with overlapping meanings here, so I'll elaborate on @sawa's answer to add some color.
しょーむない is probably a cute slangy way to say しょうもない, which is a common contraction of しようもない, which means "silly" or "useless". This is mainly used in western dialects, and the standard would be しようがない (often contracted to しょうがない) or くだらない.
しようがない, however, also has the meaning "there's nothing we (you, I etc) can do about it", similar to しかたがない. In western dialects, this might be expressed as しゃーない, and I'm actually not sure which one of the above this is a contraction of.
There is also an expression どうしようもない (どうしようもない) which does not have a particularly dialectal feel to it, and can mean both "silly"/"useless" or "there's nothing we can do about it".
Finally, there is no どうしようがない, since the どう requires the も, but どうにもしようがない is common as well.