Straight means going in one direction only without deviation. Alternatively it’s used for something level or symmetrical. To straighten is to put into proper order or condition.
Straight up, implies honest and direct, unless it’s a drink in which case it would be undiluted. A straight-laced person is conventional and respectable.
I had my hair straightened once. What do you think? Did it make me look straight-laced? Should I have changed it straight away?