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After the wedding, Hermione has to use a memory charm on two Death Eaters, where she states that she has never done it before, but she knows the theory. However, she states that before she left on her adventure, she made her parents forget her, and move to Australia. Is this a contradiction, or is there an explanation?

I don't believe it's directly addressed in the stories, but Hermione indicates things about her parents' substitute life, such as the fact that they don't have a daughter; this suggests that she didn't use the Obliviate charm, but something more complicated. Obliviate COULD remove the knowledge of them having a daughter, but at the expense of the last 17 or so years of their memory, from how it's shown being used. (Or, possibly, just the 'event' of her birth/life/etc, but that would still leave too many loose ends.) This is far from the first time we've seen her use a spell that hadn't been specifically "taught."

So this could be the first time she used that specific memory charm; that being one that simply wipes memory of a certain time period or event.

Also, she later says "I’ll find Mum and Dad and lift the enchantment," but Obliviate appears to erase memories, rather than simply hold them suppressed, so what would there be to lift?

That's trying to stick to the story. What I suspect happened is that JK Rowling did some re-writes or editing, and missed that :)

To quote from a webchat from JK Rowling shortly after the release.

Laura Trego: Did hermione really put a memory charm on her parents she
says she did but then about 50 pages later tells ron shes never done a
memory charm

J.K. Rowling: They are two different charms. She has not wiped her
parents’ memories (as she later does to Dolohov and Rowle); she has
bewitched them to make them believe that they are different people.

So, it looks like the movie's use of obliviate was wrong, but the book was right. They just were two different charms, although related, different. That might also explain why it was possible to reverse the charm on her parents.

Hermione used a Confundus charm on her parents, and bewitched them to think they were different people. She never used the Obliviate (memory) charm before using them on the Death Eaters.

She modified her parents' memories rather than erasing them. The Memory Charm erases memories, which Hermione had never done. In the movie, she used Obliviate both times, but she also never claimed to not have done that charm before (I think).

It was likely Confundus. There are uses in the book that I can think of at the top of my head. First use was Hermione using it on Cormac to make him move in the opposite direction. This is very different from another use where Snape under Dumbledores instruction to make Mundungus Fletcher think he came up with the 7 potters Idea. This use seems directly related to modifying memories. So with both uses I’d determine that Confundus is used to confuse the brain. This seems like it can be used for a variety of things. In theory it could be used as an alternative to at least 2 unforgivable Curses. One might convince the victim that they are suffering extreme pain, another use could essentially brainwash the victim into doing the users bidding. In theory a skilled yser could perhaps even kill with it by confusing the brain into stopping the heart, all in theory.