They will only "be nervous" if you act nervous.
They will love you to pieces and melt in your arms, even if you have died your hair pink.
All you gotta do is get down on their level (size-wise, eye-contact-wise), and let your eyes get as wide with joy as your heart will feel at seeing them, and do a lot of Oooohs and Ahhhs, I'm so thrilled to see you again, etc. And say it (and hug) to each daughter individually, of course, not as a "trio" or "group."
Then as quick as possible, once everybody has settled in, get rid of all other company that may be around, and invite all three of them to come sit somewhere cozy, on a carpeted floor, or huge couch, or even on top of the bed where all three can sit very near and be warm, honest, sincere. Have some popcorn or something while chatting. Then give them as much info as you can for their ages, and BE HONEST.
Play up what you may STILL agree with (ie, still believe in God? the Bible? or things like that). If so, play it up. If not, then, hmmm, think of something you CAN still agree on, etc. In other words, dwell on the positives vs. negatives. OK to explain negatives, but play UP the positives moreso.
If they act "funny" at all, it's only because, like you said, they may not KNOW what YOU are thinking/feeling, but as soon as you show them "all is SAFE" and you are STILL a "safe place to fall" (to borrow a Dr. Phil phrase), then I think they will melt in your arms and snuggle up to Dad like it was very natural to do so, like there was no time lost whatsoever.
The oldest may be near the "age or hormones" so she might be a little aloof for that reason if nothing else, so keep that in mind, too.
Never ever act like you are "afraid" of them (fear of what the other family may have said about you in the interim years that may have affected the girls, etc.)
Even if they act aloof, DON'T buy into it. Ignore it and keep being warm and loving.
I hate to bring up a proverb that was often used by the WT, but it's so true...
The heart is as a well of deep waters, and the wise person will DRAW IT UP.
So "draw up" the feelings of each girl individual and give them time to express their feelings.
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I'm no expert, just going from the heart, remembering what it's like to be a kid and around parents who didn't talk, and parents who dealt with us as a "herd" rather than as "individuals," etc.
HTH and I bet it will all be fantastic!
Let your Warmth and Wisdom shine through!
/abbagail