This is my weakness too. I plan to do a ton of practice SATA before I test on monday. One piece of advice is to make each statement a true or false statement and go from there. That has helped me with some questions, hopefully it will help on NCLEX.
I think that SATA really boils down to knowing the content. There's not a universal "strategy" that can increase your chances of getting these questions correct apart from knowing the content. I doubt that "practicing" tons of SATA questions apart from reviewing content will increase your SATA scores. SATA questions are designed to determine if you know the content well enough to know which statements DON'T apply as well as the ones that DO - which requires more detailed content knowledge than simply being good at taking an educated guess on a multiple choice question. The one thing that does help you from becoming overwhelmed when you see all the boxes on the screen is to approach each answer option as a separate statement. Treat each answer like a true/false question, then move on to the next statement. The most important thing is to correctly identify the topic of the question before you even begin looking at answers. Are you looking for correct info, or incorrect info (ie, "the pt needs further instruction")? But honestly, don't get stressed out that your average on SATA questions is significantly lower than your average on multiple choice. The test designers are fully aware that SATA questions are harder and they expect even the best students to score significantly lower on these questions. My overall Kaplan Q-bank average was 73%, but I took a Kaplan test that had only SATA questions and I scored around 33%, and I still passed nclex with only 75 questions.