What is the studio's goal when making a sequel to famously horrible movies (aside from making money)?
There is none aside from making money. From the Wikipedia article on The Asylum:
As of 2009/2010, The Asylum have never made any losses from their film productions.
My guess is that their techniques come directly from the playbook of director Roger Coreman. In his autobiography How I Made A Hundred Movies In Hollywood And Never Lost A Dime he talks about his techniques for making low-budget movies.
Director Rob Cohen (creator of the Fast & the Furious franchise) gave a great interview where he discusses working on The Boy Next Door where he used similar techniques. (I can't find the link for the interview right now, unfortunately.) He talks about how you can make a movie on a very low budget by taking all sorts of shortcuts, like ensuring that extras like a waiter in a restaurant don't speak at all, and similar things.
It sounds very much like these other low-budget sequels are building on the same techniques, with possibly slightly larger budgets. As far as the Asylum is concerned, they go so far as to have audience polls to figure out what people want to see. At the end of "Sharknado 3: Oh Hell No!" they asked viewers to decide whether Tara Reid's character lives or dies:
A note then appears, inviting the viewing audience to register their votes at #AprilLives, #AprilDies, or Sharknado.Syfy.com as to whether April survives, the results of which will be revealed in Sharknado 4.
This makes it pretty clear to me that the point is to simply to service the audience in whatever way possible. If the audience wants cheesy movies with implausible plots and bad special effects, then that's the purpose of the sequel. If they want something else, then that's the point of the sequels. It's pretty much cinematic pragmatism - give the audience exactly what they want and are willing to pay for.