Stormtroopers are considered the elite force by Imperial standards. And yes, they work as squads. If you notice in the movies, there were small squads on the Tantive IV (the squad that captured Leia was four troopers) and on Cloud City.
Stormtrooper unit organization was separate to that of the Imperial Army and Navy, although this elite unit supported both arms of the Imperial Military. They followed similar organization patterns: squads, platoons, companies, battalions, regiments, and battlegroups (called legions).
The majority of Stormtroopers actually are clones. They're clones of random political people and their cousins, etc. Then there's also some enlisted and drafted.
Star Wars Insider #76
During the production of Episode III, Lucas told crewmembers that the stormtroopers seen in Episode IV are - in the story world - made from multiple sources. That is, they're not all Jango clones. By that time in the saga, other clone hosts have been selected.
Lucas intimated that the selection process has become more political than strategic in some cases - a highly placed officer's cousin might be selected over a more capable specimen, for example.
In addition to multiple clone hosts, stormtrooper ranks also include conscripted soldiers and academy graduates, as his been chronicled in the Expanded Universe for many years now.