Musical Style (Videos Below)

The style of music Dethklok plays can be described as "melodic death metal." 
Vocals: Nathan Explosion's lead vocals are generally "death growled" rather than sung or screamed, and the lyrics often deal with morbid topics such as hatred and death (one noteable exception being "Duncan Hills Coffee Jingle"). Cleaner background vocals are often used as well and are sung by the drummer; Pickles. 
Drums: Drum parts are often very fast and usually characterized by strong double bass drum and heavy use of crash cymbals.
Guitar: Skwisgaar Skwigelf's lead guitar parts usually alternate between palm-muted power chords in low tunings (usually low C, although sometimes drop D is used) and mid-range, single note riffs. Solos and interludes are generally very fast melodic lines that utilize many virtuoso techniques including sweep picking, shred picking, and pinch harmonics, but also occasionally include slower parts and string bending. Toki Wartooth's rhythm guitar parts generally provide a chordal background for the lead parts, but occasionally will double or harmonize more melodic lines, especially when they are repeated several times.
Bass: Murderface's bass guitar parts usually consist of chord roots, but are often mixed out of songs entirely. Shown below are some examples: