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There are many articles on Johannes Nordström’s web page.
Here is another article with some more examples. They construct two G2 manifolds which are diffeomorphic but whose G2 structures are not homotopic, hence the title of the article.
Mark Haskins is another expert on G2 manifolds, though I can’t seem to find his webpage.
NB, I don’t lack articles with examples, what I currently lack is the leisure/energy to extract them into the $n$Lab page.
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