The screen (or the window if doing TWR) is more important than the strip bay! Having said that, it's possible to claw yourself back from an overload situation using your strips, if you can trust your strips.
The best thing is to try making a positive action with the strips at the same time as giving the pertinent instruction. It's easier in the aerodrome environment, where for instance you can move a strip into the runway bay as you say the word "cleared", followed by "for take-off" or "to land." In the approach/terminal environment, the ideal is to write as you speak, preferably without looking down too much.
Different units (and countries) have different ways of ordering strips for radar control. Area/enroute strip movement is a dark mystery to me, but as a UK-trained approach controller I tend to have strips in landing order for arrivals, the first at the bottom, or in order of cleared altitude where appropriate, the highest at the top. Departures go up the bay as they get further away from the runway (the opposite is true for Canadians as an example). The crux though, is to have strips for conflicting aircraft next to each other. As you remove the conflict, you move the strips to indicate that the confliction is gone.