Hi suededevil, and welcome to the board!

"Eke out a living" means to make very little money, just enough to barely pay the bills, and usually not with a very secure employment. Maybe small jobs here and there.

"Earn a living" implies more of a steady, comfortable employment and income situation. If you "earn a living' you are usually doing okay financially.

"Strive for a living" would seem to imply more of an awkward situation than "eke out a living", since if you're striving for a living you're struggling to achieve a level where you're ekeing out or earning a living. But some folks who have steady work may not consider themselves to be living a solid , comfortable lifestyle on the money they earn, and might say they are striving to earn a real living.