The events of Star Control II are part of a major war between the established Ur-Quan Hierarchy and the atavist New Alliance of Free Stars. Several races are not aligned with either faction, but still interact with the members.
The Druuge are shrewd businesspersons, first and foremost. They appear to have avoided Hierarchy membership by selling-out the neighbouring Burvixese while maintaining relations with the Utwig. The Captain can have a range of interaction with them, including slave trade, barter and war, but the Druuge remain well outside of both the Alliance and the Hierarchy.
The Melnorme are a transient and inevitably successful people who trade in advanced technology and intelligence. They can be a major help to the New Alliance without entering any formal agreements, and it was them who sold the ill-fated Probe to the Slylandro. There is no reported interaction between the Melnorme and the Hierarchy worlds. The Melnorme have no Sphere of Influence.
The Orz arrived in our corner of the galaxy after the war between the Hierarchy and original Alliance, and are thus neutral. Depending on how many questions The Captain asks them about the Androsynth, they will either join the New Alliance or attack The Flagship, but they will not join the Hierarchy.
The Slylandro are a gaseous people who live extremely long lives and cannot leave their homeworld. They tell the The Captain about receiving friendly visits from the Precursors, the Ur-Quan and, more recently the Melnorme and Humans. The Slylandro have no Sphere of Influence.
The Spathi wanted to be slave shielded in order to follow a policy of isolationism and neutrality. Due to a communication error, they became Battle Thralls, but then defected to the New Alliance at their first opportunity and used the relationship to study the Slave Shield around Earth, which they replicated at Spathiwa.