Riding stunts such as "wheelie," "stoppie," or "drifting" are considered reckless driving when performed on public streets.
All three words are rather informal/slang, and I'm afraid that they are not suitable for academic writing. Are they? Should I use quotes as seen above to mark that they are informal/slang, hence making them usable in academic writing?
If you need to use a word from the jargon of a particular activity which has a specific definition within that activity, by all means use it. The quotation marks show, not so much that it is 'informal', but that it has a special meaning in this context.
(I don't know what drifting is in the context of cycling, but it also has a meaning in standard English!)
It's OK to use jargon or slang in academic writing, but you should define what those words mean, in context, somewhere in the document. Depending on the type and style this could be in line parenthesis, a numbered footnote on the page or in an appendix, or even a glossary if there are a lot of such words. This applies both to normal English words used with a special / unusual meaning (such as "drifting") and jargon words with no normal usage (such as "stoppie").
Since anything can be studied academically, including things that are socially informal or offensive, academic writing might need to talk about words or usages that it wouldn't actually use. There are entire books that trace the history and sociology of a single word so offensive that casual public use would get someone fired. And you give a great example of a case that might be inoffensive but colloquial, addressing slang terms in formal writing. Yes, using such terms is not only acceptable, but the best choice when there is no easy formal equivalent. For instance, if you need to say "Operating this machinery while drunk is prohibited," then "drunk" is fine and there's no need to use colloquialisms like "hammered" or "shitfaced." But there's no easy formal equivalent for "wheelie," let alone things like "ghost riding the whip," so it's best to use these terms when discussing them. As Peter suggested, it's best to also explain them when they're not common knowledge. If you're going to use a phrase repeatedly within a short section, it might be best to use quotes only on the first instance. After introducing and explaining it, it might be reasonable to leave them out.
On the other hand, it wouldn't be a good idea to use casual colloquialisms, with or without quotes, when they're not integral to the discussion, depending on the level of academic formality. For instance, in a scholarly work, I wouldn't write "By 18xx, Admiral Smith's colleagues generally saw him as having 'jumped the shark,' as it were." But I might if I were writing an opinion essay, or a piece aimed at making history accessible to a general audience, especially if Admiral Smith had had a famous encounter with a shark.
Finally, I should say that I've received advice in academic writing saying to avoid overusing "scare quotes." This is mostly a different matter, but related. The point of quote marks, in general, is to say "these are not my words." In your example, it means "I'm using the word 'wheelie,' but only because other people do; I don't own it as part of my own writing here." "Scare quotes" are similar, but might be applied to words or phrases that would be perfectly reasonable to use; instead, the author is distancing themself from their meaning. E.g. "Indigenous villages are being increasingly overrun by tourists seeking an 'authentic' experience." The author means that the tourists might describe it as "authentic," but it's such a notion is problematic and the author doesn't necessarily agree with it. General writing advice is to minimize the use of such scare quotes. To me, I don't think it's reasonable to eliminate them entirely, but they should probably be accompanied by explanation just like the colloquialisms. And a general principal for both kinds of quotes would be, use them if you need to, but if you find yourself using a lot, ask whether you really need to.
