Strong abdominals does help with your lower back. This is because if you have any excess weight in your midsection, and you have weak abdominals that don't support the weight, it will pull on your lower back.

The best thing to do is strengthen both muscle groups.

Since you do not have gym access, the best way to strengthen you lower back is an exercise called a Straight-leg deadlift. Normally this is done while holding a barbell, but you can use a broom, or other stick-like device to hold instead of a barbell.

To perform a SDL , you stand straight up .... shoulders back (so you look like you are sticking out your chest). Now, slowly bend from the waist until the bar is about knee level. IT IS IMPORTANT TO KEEP YOUR BACK FROM ROUNDING -- if you keep your shoulders pulled back, it will not round. When you are at knee level, slowly come back up to the start position and do it again!

For abs, the exercise you mentioned is great. I call them "bicycle crunches" and yes, they are effective. Give them a shot!

When the SDLs with no weight get easy, try adding weight. Use ANY form of weight you can. Gallon of milk, growing child, favorite small pet, WHATEVER. Just be sure it takes about 3 seconds to go down, and three seconds to come back up.

Let me see if I can get a link to a picture of this exercise ....
OK, no direct link, but go to www.strengthcoach.com. Once you get in, click to GO TO VIRTUAL WEIGHT ROOM. Then, choose LOW BACK. Next, choose Stiff-leg Deadlifts. When the stick figure appears, click ACTIVATE.

While you are there, check out REVERSE HYPERS for low back.