strive after something
to try very hard to obtain something. I am always striving after perfection. Ted was striving after a promotion and finally got it.
strive against something
to work against something. He worked hard, striving against failure at every turn. Things were difficult. I had to strive against quitting almost every day.
strive for something
to try to obtain or bring about something. I am striving for the best possible result. Mary strives for perfection in everything she does.
strive to do something
to try hard to do something. She strove very hard to do what she had set out to do. Please strive to do it as best you can.
strive toward something
to work toward a goal. DI always strive toward perfection. Mary strove toward doing her best at all times.