sway bars help keep both tires on the ground during cornering. during a hard turn, the inside wheel will want to rise up, since the outside wheel is compressed. a sway bar will counteract that (or do its best to) and keep both wheels on the ground.
read this writeup
http://www.clubcivic.com/board/showthread.php?t=13203
it is long.. yes, but it is a great writeup iamgod did a while back. it will help you understand whats going on... even if you dont understand everything that is covered.
strut bars help keep the body rigid under corners, and somewhat reduce body roll.. but mainly body flex. they basically make the two shock tower assemblies and tie them together, so they act as one, and dont move separately when cornering and such. they basically help make the car more stable.
however i would do some more reseach before automatically getting all four strut bars... and sways... they can have some strong effects on the dynamics of the car. your understeer/oversteer are the biggest things effects by these mods so just take it easy if/when you get them... dont go haulin ass into a turn until you have a good feel for the car with these mods.