I feel sort of silly replying to this, because I'm a total beginner myself, but I was just going through the same thing as you (very frustrating!) and I recently made a bit of a breakthrough, so I thought I'd share what worked for me.
First of all, I had been strumming sort of parallel to the uke, if that makes sense, so that my index finger was hitting the strings on the sides of my finger/nail and I was getting caught up in the A&G strings as I moved my finger up and down.
Then I switched to strumming 'up-and-down' with my finger perpendicular to the strings. With my pointer finger curled under loosely on the way down, the nail of my pointer finger brushes the strings on the way down, and then on the way up I let the pad of my finger brush the strings (keeping my finger loose), and that seemed to help a lot. Nail on the way down, pad on the way up. No more catching.
It's harder to explain clearly than it is to do! Maybe it's incorrect form, but it seems to work for me, so I'm going with it!!
Another thing that helped was watching a few basic strumming tutorials on Youtube.
Finally, a HUGE breakthrough for me was using an online metronome (like this one:
http://www.metronomeonline.com/ ) and doing nothing but strum for 10 or 15 minutes straight without stopping, other than to change the tempo occasionally. You can do this with your left hand muting the strings so you can concentrate on rhythm and not worry about the sound of the strings. If you do this a couple of days in a row, you'll definitely improve! I did, and I'm definitely not a musical genius by any means