A few suggestions, based on the additional comments you've made...
Since this seems to be a work thing, can you put up a couple of photos or something in your work space?
With the non-confrontational thing, instead of "Google me, motherfucker...", you could actually sort of manipulate them into Googling you. "So I met this girl through OkCupid and we had a dinner date. We're sitting there eating and she says, 'you know, I Googled you before I came. I was really surprised to see that (article, website, news report, whatever) about you.' I don't think I'm going to go out with her again... I dunno, it's just weird to have my life laid out via Google to some chick before we've ever met face-to-face, you know?" You can bet they're going to hit Google as soon as you walk away.
Ask one of them, privately. "hey, you and so-and-so are often making comments about how you think I'm telling stories. Look, I'll be happy to prove what I've said to you, but in exchange, maybe you could explain to me WHY you guys always seem to think I'm lying." And then be prepared to show that person your proof AND to hear their explanation fully, even if it's a bit insulting.
I can tell you this - one of my friends ALWAYS sounds like she's lying. I mean, she can be sitting there telling another friend about something she and I did together, and I'm sitting there listening to her retell our trip to the craft show and it's 100% accurate, and she sounds like she's lying even to MY ears. LOL It's just the way she talks... her avoidance of eye contact (her eyes shift CONSTANTLY)... and her body language. She also fidgets a lot with her hands, and there's these sort of odd pauses when she's talking, like the kind of pauses you'd expect when someone is thinking up a lie. It's also her inflections, like her voice goes to a higher pitch after one of those pauses and she sort of rushes out a sentence.
She actually got fired when her mother died, because her new boss thought she was lying when she called to say she wouldn't be in. Catholic family, so after the funeral and such were over, she went back to her office with the Mass Card and obituary and got her job back.
But she knows about her problem. Knew about it long before I met her. She can't even say, "I'm 48" without you thinking, "yeah, sure you are." LOL Ok, it's not QUITE that bad, but yeah. It's sort of funny and a little tragic all at the same time.