I am currently writing music and I am looking for a similar tone to these bands.

I know that Moose Blood don't really use pedals and just use an orange dual terror but I am looking for a hybrid kinda clean but also nice dirty tone like on the Basement track so would a dual terror and an overdrive pedal over that?

Would there be any other pedals that people would recommend for an emo/grunge/rock type sound.

The first example sounds much more like an American amp driven to death. I do see a HiWatt in the background though. The second example sounds much more British. The Dual Terror would easily get you that kind of tone in the 2nd video, for the 1st video you might need to scoop the mids a bit.
carbiscoffee Yeah, you should be able to get there with the Dual Terror fairly easily. Assuming you were gigging both songs, I'd just use a tubescreamer in the front and use the fat channel for most of the heavier overdriven stuff, with the tiny channel for cleaner stuff. I'd also use a simple EQ (e.g. Boss GE7, MXR 6 band, Behringer EQ700) in the loop to scoop out some mids too.

Should be pretty easy with the amp alone though