Unsurprisingly, the main practical uses of auxlangs are linguistic. Two are relatively well known:
1. First Foreign Language. Esperanto, at least, (and perhaps other auxlangs) can be learned first to speed and ease language acquisition in general. It's a pity this hasn't been attested for other auxlangs, so far as I know, but then Esperanto's adjectival agreement and accusative marking should be especially helpful for those whose native language lacks such traits.
2. Introduction to "International Vocabulary." Not a strong point for Esperanto, but a long-standing strategy for mainstreaming Interlingua in Scandinavia in particular. Instead of learning isolated roots, students can learn roots in a more organic, natural context. This could also be done with Occidental and, to a lesser extent, Lingua Franca Nova. For that matter, Sambahsa could be used for learning western roots in general (and some non-western ones, too), though perhaps at a higher level of abstraction than a beginner would find useful.
There are other possibilities as well. I would suggest Ido for people wanting to learn about linguistic precision--not as jarring as Loglan, for example.
Dave MacLeod has occasionally advocated starting a news site in Occidental or Interlingua. I think (cynically) that a celebrity-gossip site would do better, but using an at-sight language for some kind of information clearinghouse is probably a good idea.
It might also be useful to provide a translation of a European or Latin-American site in Interlingua or Occidental. Properly set up, it will draw some visitors via search engines, and the attention could be useful--so long as copyrights are respected. If the auxlang version is a faithful copy of the original, I doubt there will be much trouble.
What matters in any case is to get the word out--and remember, even if the auxlang that gets the initial publicity isn't your favorite, the improvement in general attitude toward auxlangs will help your favorite. As I've pointed out at various times, anyone who looks up Esperanto on Wikipedia will find plenty of references to other auxlangs too.
Next up, we'll look at the complex issue of proving auxlang superiority.