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
I am afraid that there are no solution that fits all need. All have drawbacks and advantages.
Accents, if you can do them, work great. Pick a real life language and use an outrageous accent of the same for your Blurbnish. Clearly, the more outlandish and caricature the accent, the better as long as it fits the tone of the game. If the game is real life, then use the real life accent. Another related note is to use words in a real life language within the sentence but that gets complex and unclear quickly.
While some real life accents may be seen as or are racist and offensive, I shall leave it to you and your group to work out one that is not. Follow Wheaton's rule: don't be a dick. If this is really a problem for you, why not invent an accent?
A potential problem with accents, as SevenSidedDie pointed in a comment, is that no one can have accents while speaking a foreign language without being confusing.
Another language, if you both speak a different language, you can use that. Of course, it requires you to be fluent in more than one language. Maybe even use something like Pig Latin.
A prop, like a hand gesture, cards, or a hat. Hats got quite silly so we stopped using them fairly quickly but your mileage might vary. You could use cards or other visual cues but then you have to remember to swap them out and it could get messy with lots of languages. Hand gestures mean that the other players must see you which can lead to confusion if they do not or just miss the cue.
Another prop that might be useful is a small set of flags those country uses the language. This works for real and imaginary worlds but might make your gaming table look like an unholy meeting of the UN...
Just to stop the downvote faerie: Yes, I used all of those in games before. Yes, they worked great. No, no one was offended at my outrageous French accent or at my attempts at butchering English or my silly hat.