2378

Events

Q leaves his son temporarily in the custody of Kathryn Janeway hoping that her Starfleet ideals will correct his negative behavior. (VOY: "Q2")
Communications between Voyager and the Alpha Quadrant improve when real-time communication is made possible. (VOY: "Author, Author")
Lieutenant Joe Carey is killed while on an away mission to retrieve the Friendship 1 probe, which had contaminated the planet Uxal in the Delta Quadrant. (VOY: "Friendship One")
Neelix departs the USS Voyager to live with a group of Talaxians living in an asteroid field; he becomes the permanent Federation ambassador in the Delta Quadrant. (VOY: "Homestead")
Lieutenant Ayala transfers from the operations division to the command division aboard the USS Voyager. (VOY: "Renaissance Man")
Captain Kathryn Janeway is captured by the Hierarchy; Voyager's EMH has to masquerade as the captain in order to save her and protect the crew. (VOY: "Renaissance Man")
Seven of Nine and Chakotay begin dating. (VOY: "Endgame")
Voyager detects high levels of neutrino emissions inside a nebula in the Delta Quadrant. A large Borg presence is found inside and the crew initially avoids it. (VOY: "Endgame")
A future version of Kathryn Janeway arrives from the year 2404 to aid Voyager in using the Borg transwarp network to return to the Alpha Quadrant. (VOY: "Endgame")
One of six Borg Transwarp Hubs is destroyed by the crew of the USS Voyager during her successful return trip home. The future Admiral Janeway remains in the Delta Quadrant to introduce a neurolytic pathogen into the Collective. The assault cripples the Borg and makes Voyager's escape and use of the transwarp hub possible. (VOY: "Endgame")
Miral Paris, daughter of B'Elanna Torres and Tom Paris, is born during Voyager's trip home. (VOY: "Endgame")
In an alternate timeline, Andrew Kim was born to Harry Kim and Linnis Paris. (VOY: "Before and After")

Notes

Given that "Endgame" takes place sometime after "Homestead" (which in turn takes place on the 315th anniversary of First Contact), and taking Seven of Nine's statement in the former episode that the events of "Human Error" take place three months previously, we can conclude that the episodes from "Human Error" to "Endgame" take place in this year.
The United Federation of Planets has 183 members and 7,128 affiliates. (Star Trek: Star Charts, United Federation of Planets IV)