The campaigns are unique to each expansion. Buying Legacy of the Void will not give you the Wings of Liberty or Heart of the Swarm campaigns. However, all multiplayer features from prior expansions are included in the latest expansion. So Legacy of the Void will allow you to play with the units introduced in Heart of the Swarm.
Note that some of the game rules differ between the expansions. For example, playing Legacy of the Void multiplayer, you will start with 12 workers and have a higher starting supply. The other two games start you with 6 workers. Some unit abilities also vary between expansions.
- If not: Is there a story-line in common and is it in chronological order?
There is a common story line between the three games. It is also in chronological order: Wings of Liberty -> Heart of the Swarm -> Legacy of the Void.
- Does any of them introduce new units/buildings/technologies/features?
Each expansion has introduced new units, technologies, and features.
Heart of the Swarm brought Terran the Widow Mine and the Hellbat, Zerg the Swarm Host and the Viper, and Protoss the Mothership Core, Oracle, and Tempest. You can see more details at the official game guide.
Heart of the Swarm also brought a new profile leveling system, where you gain experience during a match for resources you spend and enemy units/structures you destroy. Gaining enough experience will grant you a level in whatever race you were playing, unlocking cosmetics like portraits, decals, unit skins, and unit dances.
Legacy of the Void again introduced new units. Terran armies gain the Liberator and Cyclone, Zerg the Lurker and Ravager, and Protoss the Disruptor and Adept. More details are in the official game guide.
Legacy of the Void also introduced automated tournaments and two new game modes. Archon mode allows you and a friend to team up and share control over the same base/army against another pair of two players on one base. Co-op Missions allow you to choose one of six heroes and team up with another player to complete one of five objective-based missions, leveling up your hero and unlocking perks for your army. Note that you can actually play Co-op Missions without Legacy, but you're limited to just the first three heroes (Raynor, Kerrigan, and Artanis).
- Will there be more expansion packs?
No new expansion packs have been revealed, but Blizzard has announced plans to release small campaign DLC in the form of mission packs. The first of these, Nova Covert Ops is planned for Spring 2016.
In addition, Blizzard has announced ongoing support of the multiplayer game, including unit balance and a revamped ladder system (in the works for 2016).