To be honest, I'm kinda mystified why so many punkeroos love Times New Viking. I mean, it makes me happy, but it's kind of weird.
To me, they are straight-up modeled after vintage early 90s "indie rock," from stuff like early Slay Tracks Pavement and good fried Sebadoh and things of that ilk (K and KRS type shit) to more noisy shit like old Sitlbreeze yarns (obviously) and something like Shrimper cassettes and 'Popwatch'-y shit like that. Throw out all the UK post-punk/DIY comparisons you want, but you people are listening to what indide rock was at its finest. Maybe it's time to reinvestigate?
Now, on a musical level, it's all about: shaky opff-key/kiler boy-girl harmonies; really sweet melodic riffs that twist and bend and break and sound awesome/fucked-up fidelity-wise; hissy production that actually compliments the music instead of obscuring it;
Also, don't underestimate things like coolness/fashion/graphics/etc. That they are able to stradlle fences of genres (indie/punk/noise/homerecording) is interesting and healthy.
They are stoner-friendly.