I think they know, but they couch it to themselves in their own internal narrative as like… just the way they choose to present themselves as per their preferred “cool” subculture (how others see their “cool” subculture is another matter entirely).

(Details below the cut)

Let’s start with Hermann. I’m 100% convinced Hermann knows he is an eccentric and embraces this ideal about himself. But what kind of eccentric he thinks he is is very different from how other people see him. He sees himself as like… Oxford professor, throw-back to the days where people had culture, damnit. His heroes were WWII era scientists like Alan Turing and by God, he knows his place in history and he’s going to live up to it. I think he misses out on the part where like… wearing slacks that aren’t tailored quite right and granny glasses makes him look less “respectable academic” and more “cosplaying your grandmother”. He’s trying so hard to be this intense, serious academic, and comes across a bit ridiculous as a result. Like how he makes his rants like the “Handwriting of God” speech deadly serious, and seems to have zero irony or awareness that other people are literally “wtf-ing” behind him and even Stacker is kinda ??? about why this subject came up at all. He’s very intense, very earnest, and completely unaware that no one else really sees him as he sees himself. 

Meanwhile, Newt genuinely thinks of himself as a rockstar. He dresses like a member of Good Charlotte circa 2005 or maybe just like one of the Blues Brothers. He’s got the tattoos and the glasses. He’s painfully hipster (god I bet he ironically drank PBR in Boston before the Kaiju landed) with that nerd subsection of being at least mildly otaku-ish with the Kaiju obsession thing. He definitely loved the concept of Kaiju before it was cool, i.e. before they showed up for real. He buys into his own rockstar image buuuut, like Hermann trying to pull off the “respectable professor” thing I’m not sure Newt pulls off the “rockstar vibe” to the extent he’s aiming for it, given he comes across as more “hyperactive and shrieky”, and I think his attempt at “ironic nerdom” with the glasses and tie are just seen as “actually nerdy”. 

To the second half of your question,I think in the last days of the Shatterdome under Pentecost you had a lot of big personalities. People to whom being part of the “The Resistance” was more important than, say, being paid, or just living out the final days of Earth with their loved ones. Everyone is kinda eccentric and aware of their own importance in that Shatterdome. It’s the opposite of a faceless organization (and probably a lot of that is GDT going by “The Rule of Cool” – everyone is really, really cool). But I also think Pentecost let a lot of regulation go by the wayside so he could recruit these best and brightest, and for Newt that was certainly a draw, who likes to march to the beat of his own drum and respects people who let him do that. Whereas for Hermann I think it was more about Doing What Must Be Done, especially after his father backed the Wall of Life, he had to make a stand with the person making the biggest stand.