Rockstar released two standalone episodes for GTA IV. They do not follow the main story; they run alongside it and cross it several times from another perspective.
Both released in 2009
Protagonist: Johnny Klebitz
The story of the vice-president of The Lost motorcycle gang. It runs alongside the main game and crosses it several times.
The darkest of the three. It shows the same events from another side; places merely passed in the main game have a purpose here.
Protagonist: Luis Fernando Lopez
Nightclubs, parachutes and explosions. The most colourful and entertaining part of the package.
Anyone who finds GTA IV too grey should begin here. It is the same city in an entirely different mood.
If the main game's tone suited you, start with The Lost and Damned; it is similar but darker. If it felt too grey, begin with The Ballad of Gay Tony: the same Liberty City, but with colour and humour otherwise absent from GTA IV.
Both episodes can be played independently. Knowing the main story is not required, although some references make little sense without it.
GTA IV has a reputation as the poorest-running game in the series. There are specific causes, most of which can be mitigated.