First the definition would be good. Sadly, there are quite a few but I think that only one is important:
- Relating to the philosophy or theories of aesthetics.
- Of or concerning the appreciation of beauty or good taste: aesthetic
judgment; the aesthetic appeal of the exhibit.
- Attractive or appealing: the more aesthetic features of the building. Characterized by a heightened sensitivity to beauty: the poet and his aesthetic friends.
- Being or relating to a work of art; artistic: The play was
an aesthetic success.
- Informal Conforming to accepted notions of good
taste.
- often Aesthetic Of or characteristic of aestheticism in the
arts.
But we can agree, that if someone/something is aesthetic than it it beautiful, worthy of admiring. Or, we could go even further and replace the word "aesthetic" with "Art", which often has been treated as something seemingly alive and conscious.
Now the examples from the book:
Aesthetics will intervene: would a Napoleon really go crawling under the bed of some "old hag"! Please!'
Let me show you this in a different translation (by Constance Garnett)
One sudden irrelevant idea almost made him laugh. Napoleon, the pyramids, Waterloo, and a wretched skinny old woman, a pawnbroker with a red trunk under her bed—it’s a nice hash for Porfiry Petrovitch to digest! How can they digest it! It’s too inartistic. “A Napoleon creep under an old woman’s bed! Ugh, how loathsome!”
So it is impossible to imagine someone so great as Napoleon doing something as despicable and loathsome as hiding under a bed of some old hag - those two things are just too opposite in the aesthetics spectrum, too inartistic (it is like painting a nude act of a beautiful woman sitting on a toilet!); it is so despicable that some sort of higher force should intervene! Following this chain of thought, someone who indeed was hiding under an old woman's bed cannot think about himself as being as great (as aesthetic) as Napoleon.
2.
I'm an aesthetic louse, that's all there is to it!
Again, a different translation makes it more clear
aesthetically speaking, I am a louse
Raskolnikov keeps self-depreciating himself - it is bit more clear further on:
Ech, I am an æsthetic louse and nothing more,” he added suddenly, laughing like a madman. “Yes, I am certainly a louse,” he went on, clutching at the idea, gloating over it and playing with it with vindictive pleasure. “In the first place, because I can reason that I am one, and secondly, because for a month past I have been troubling benevolent Providence, calling it to witness that not for my own fleshly lusts did I undertake it, but with a grand and noble object—ha-ha! Thirdly, because I aimed at carrying it out as justly as possible, weighing, measuring and calculating. Of all the lice I picked out the most useless one and proposed to take from her only as much as I needed for the first step, no more nor less (so the rest would have gone to a monastery, according to her will, ha-ha!). And what shows that I am utterly a louse,” he added, grinding his teeth, “is that I am perhaps viler and more loathsome than the louse I killed[...]
So he says that he is just ugly, despicable like a louse - a parasite that lives in dirt and feeds on blood.