How can I access EDAS to see what assignments are available to me?

Ask someone in your S1 who has access to look it up for you.

SSG Aaron Marshall , like MSG (Join to see) said... typically you need to go to personnel with access to retrieve this information. Depending on your CoC, sometimes when the CSMs and 1SGs link up for manning meetings they will print off the list of available positions and what is a must fill to gain info on people they might suggest that branch place in those slots. Depending on your relationship with your CoC, you might be able to get your eyes on it. If not, S1, Branch, and Career Counselors are your best bet at seeing what options are going on within your MOS during the next few months to a year out.

Only those with the need for EDAS have access, S1, G1, etc. You can to ACT and see under your career path what is available for your MOS and rank. However, these are all positions, not just the ones that you qualify for (or don't). Branch is the best source of information about positions.