In general in play they were ignored or just treated as an abstract language with no further comment.
As to where they came from, here's an answer from Gary Gygax on Dragonsfoot!
As D&D was being quantified and qualified by the publication of the supplemental rules booklets. I decided that Thieves' cant should not be the only secret language. Thus alignment languages come into play, the rational [sic] being they were akin to Hebrew for Jewish and Latin for Roman Catholic persons.
I have since regretted the addition, as the non-cleric user would have only a limited vocabulary, and little cound [sic] be conveyed or understoon [sic] by the use of an alignment language between non-clerical users.
If the DMs would have restricted the use of alignment languages--done mainly because I insisted on that as I should have--then the concept is vaible [sic]. In my view the secret societies of alignment would be pantheonic, known to the clerics of that belief system and special orders of laity only. The ordinary faithful would know only a few words, more or less for recognition.
In other words, it was supposed to be more like religious languages, but wasn't really well thought through. It disappeared in Second Edition and was not missed.
There's no such thing as senseless violence, according to the one who commits it. Characters who kill or torture without at least an internal justification are crazy, not evil. You don't have a reason to kill people in the party or at random, so you don't. This doesn't make you nonevil.
Also remember that just because you're Evil doesn't mean you're a villain. Many Evil characters have no ambitions higher than their own survival and/or comfort; they don't aspire to great power, nor to purge the world of the target of their hate. They're just trying to get by, not so different from the rest of us.
The traditional list of Seven Deadly Sins was originally compiled not so much as a list of inherent sins, but a list of reasons that people sin. This makes it a great source of motives for Evil characters. I prefer to expand the list to nine, adding Fear as Wrath's twin in the fight-or-flight reflex, and Despair because it was actually in the original list; Sloth replaced it later.
Avarice: The key to happiness is having things. I will have it all.
Envy: I deserve it, not them. I will have it from them.
Gluttony: Pity those not at the top of the food chain. I will never be in that position.
Lust: I want to do it all, and I will let nothing get in my way.
Pride: I must be better then them: so much so that my superiority is never even questioned.
Sloth: I just don't want to do it. Let them do it for me. If they refuse, make them do it for me.
Wrath: They will never hurt me again. I will punish them for what they did, and leave them unable to do it to anyone else.
Fear: They must not be allowed to hurt me. (Note the lack of an again here: this is one of the big differentiators between Fear and Wrath, but it can make a huge difference in the character).
Despair: I just want the pain to end. Giving it to others helps.
Also keep in mind that these are core motivations. Any one of them will need to be elaborated upon. What is it? Who are they? How does the character plan to achieve this goal? Also worth noting is the lengths that your character goes to to hide her motives. Evil characters often prey upon one another's weaknesses, and while Wrath-type characters might not worry about seeming weak due to their motives, Sloth-type and Fear-type characters likely would. These folks are likely to construct a facade, often but not always based on Wrath, as a matter of posturing.
Your character sounds like a Wrath-type, with a focus on the undead. Because her main focus is on something that is not so amenable to the survival of humanity in general, she can get along decently well in society, and even be a very useful sort of person to have around. Some might even mistake her for heroic. But she has a twisted fight-or-flight reflex: any slight or injury, real or imagined, runs the risk of touching on that trauma, for reasons that make sense only to your character (if they even make sense to her). She might lash out disproportionately at small threats, or even against things she mistakenly believes to be threats, but are not.
Best Answer
Here's the problem you are having: it doesn't actually make sense for your group to be adventuring together. There's a bunch of do-gooders plus one person who actively sabotages the rest of them. Why is that person on the team? Why are they friends?
Of course the actual reason these characters are hanging out together is because the players are all sitting around the same table, and you feel it would be rude to ask her character to leave.
Many DMs will have rules for this: they'll say "please create a character that wants to do the adventure and gets along with the other characters." You might try asking your DM to enforce a rule like that.
An in-game solution to your problem would be to roleplay accurately. Have your character call the other characters together. Explain why your character is unhappy. Tell them you don't want to be part of an adventuring group with this other character any more. Tell them you're leaving, and you're starting your own adventuring party, and everyone is invited except for the troublemaker.
But in general, the way D&D games work is that you stay in them as long as you're having fun. If you stop having fun, you try and have a conversation about why you're not having fun, and see if there's a way to fix it. If that doesn't work, you leave the game and find a different game.
Good luck with it.