I am sorry you are going through such a terrible time.
But if your sisters are hell-bent on acting this way, there is little you can do about it. Unless and until your sisters are ready to act like adults and talk to you about the issue, you will have to learn to let it go and write them out of your life.
Here I will say that if you absolutely MUST get a letter to each sister, I think there's a way to do it via snail mail.
What you do is write each sister a letter and put it in an envelope; but don't address it. Then you mail the letter to a friend in another state; providing said friend with the mailing address of each sister on a separate piece of paper.
Your friend addresses and mails the letters for you, so your sisters WILL receive them and WILL open them because they will not recognize the handwriting and/or the postmark. They probably won't READ the letters, but they'll at least GET them.
Now, back to the problem at hand. Your best shot at addressing it is to speak to your parents. In my opinion, what your parents are doing is unconscionable!
Here's what I want you to do about it. When the next big holiday rolls around (one your sisters normally attend) I want you to calmly advise your parents that you plan to attend and it is up to your sisters to choose whether or not they will do likewise. Then do whatever you have to do to make that happen! (Be advised, it will be VERY difficult.)
In the meantime, you are going to have to work on your parents. As Asha suggested you do to your sisters, you should do everything in your power to make your parents understand what they have done.
If you live close by your parents, visit them as much as possible. If not, stay in contact with them as often as you can. Call and/or write every week. In the initial days of doing this, refer to your sisters and the family feud as little as possible (this is sneaky and it's not right, but they have not done right by you either; and it's now time to fight back).
Once your relationship with your parents has strengthened somewhat, begin alluding to the problem your sisters are causing. Keep it fairly general, but just insert the topic gradually into every few conversations and mention how much it hurts you and harms the rest of the family by association.
Eventually, you will have worked up to being able to talk about it in full. It is at that point that you may be able to prod your parents into admitting that they have turned the decision-making process over to your sisters and they've made a serious mistake. If they admit their mistake but still say they don't know what to do about it, tell them you have an idea and ask for their support - no questions asked, no involvement on their parts. If they agree (as I hope they will) then you just start showing up to the family functions and let your sisters deal with it.
I do want to caution you, however. Even if this should work, your sisters will most likely NOT be adult enough to treat you with the respect you deserve. (If they were, you wouldn't be in this boat to begin with.) You will find that you will still feel terrible. You may even wish you hadn't bothered. You will have to suck it up and keep going as well as keep your despair to yourself so your sisters won't know how much they've gotten to you (this will be the hardest part), because otherwise they will just ramp it up and make it intolerable in the hopes you'll depart and never come back.
Finally, there is an annual event called "Forgiveness Day" (www.forgivenessday.org). Each year, you can often find articles printed in the local newspaper about this day; perhaps forwarding this information to your family members will open the door a chink and let some sense seep into their brains.
I have no idea if what I've said offers any help or comfort to you, so let me just say how sorry I am that you are having to go through this. It is completely understandable that you feel depressed and I'm only surprised you haven't lost your temper and gone to beat the hell out of someone - I sure would have been tempted by now!
Good luck and take care, we're on your side.