Unless you really want to split hairs on a per article basis, in general, it is both.

If your subject for parody is 'news about current events', then you can argue that anything presented in the format you would expect from a newspaper, but comically exaggerated, counts as parody.

If a certain Onion article is fairly clearly a modification or exaggeration of a specific news event, it fulfills another common attribute of parody by having a specific thing it is parodying.

But sure, some of their stuff falls more into satire.

Satire more often has a more ... thorough and deliberate alteration of a base material or style, with the intention of conveying a more intentional critique of or commentary on the source, a fairly obvious prescriptive moral message, by subverting it in specific ways...

... as opposed to parody, which, by itself, doesn't really need to have a 'message', it can be just a level of exaggeration that is humorous in and of itself.

Generally, most of the Onion's produced content is both parody and satire.