The biceps brachii not only flexes the elbow, but also supinates the forearm (aka the radioulnar joint). Thus, when performing a biceps curl with the forearm supinated, you can maximize biceps brachii activation.
The brachioradialis not only flexes the elbow, but also serves to pronate AND supinate the forearm (based on initial radioulnar joint position). EMG studies reveal that the brachioradialis demonstrates higher levels of activity when the forearm is in either a neutral or pronated position.
The brachialis has the largest physiological cross-sectional area of the elbow flexors. Because it inserts into the ulnar tuberosity, it is UNAFFECTED by forearm position and thus is active during all forms of elbow flexion, regardless of forearm position.
One of my favorite ways to simultaneously hit all three primary elbow flexors is shown at the end.
Citation: Levangie, Pamela K., and Cynthia C. Norkin. Joint Structure and Function: A Comprehensive Analysis. Philadelphia, PA: F.A. Davis, 2005.