It is quite intricate. Drengur is more formal and strákur is more casual. I don't know if it helps but our national handball team is affectionately referred to as "Strákarnir Okkar" (Our boys). Even less helpful: drengur was originally encompassed both genders. In a description of the wife of Njáls Þorgeirssonar (of which Brennu-Njáls saga is named), Bergþóra Skarphéðinsdóttir it is said "hún er drengur góður" [hún er = she is] and [góður = good]. Drengur meant kind or just a 'well made human'.