The Empire powers are mechanically allied. The Federal powers are mechanically allied. This means that if you are pledged to one and assault the other, you will be penalized. All other powers are mechanically neutral. As noted by Martin, relationships beyond that are not reflected in-game, as they are based on the attitudes and agreements of the organized communities supporting given powers.
Powerplay has a complex political landscape regardless. I am part of Patreus, so assume my biases accordingly.
ZYADA
ZYADA is an alliance between the four Imperial powers and Yuri Grom's Euryale Gaia Union. ZYADA is at war with the Federation and Kumo Crew and is cordially neutral with all other powers. ZYADA makes an effort to respect all neutral powers as equals. Individual ZYADA powers have different histories with the other powers, but are politically unified.
Federation
Winters are politically allied. They work closely with the Kumo Crew on combat operations. Considering that the Kumo Crew has lashed out at Sirius and Antal without cause, this has probably created some diplomatic issues for the Federation.
Alliance
Mahon holds the most territory, as has been the case for case for many, many months. Mahon remains neutral to all powers. Cordial with ZYADA and the independent powers. As Vectron stated, the Alliance has a "somewhat strained" relationship with the Federation which "probably classifies as strained towards hostile."
Kumo
Kumo stammers that it is alone in the galaxy, but this is more for their mythos than anything else. Every other power knows that Kumo is the Federation's only ally, as has been the case for nearly two years.
Sirius
Sirius has historically been neutral to all powers. There are a lot of complex stories here, but Sirius was recently attacked by Kumo, and used this as an opportunity to withdraw from many systems in a broad restructuring.
Antal
Also historically neutral, but as a combat power Antal sometimes competes with other powers for expansions. This has not usually created long-term issues between Antal and other powers. Antal recently rebuffed a massive attack by Kumo and forced a ceasefire.