You don't have to read the other Mirror Universe novels to understand what happens in "The Soul Key". It's another Star Trek book where anything you need to know is pretty much explained as you go. However, if you wanted to read / watch the other Mirror Universe entries they'd go something like this:
2063:
01 Enterprise Episode: In a Mirror, Darkly, Part I (Teaser)
2155:
02 Enterprise Episode: In a Mirror, Darkly, Part I
03 Enterprise Episode: In a Mirror, Darkly, Part II
04 Glass Empires: Age of the Empress
2156:
05 Shards and Shadows: Nobunaga
2248:
06 Shards and Shadows: Ill Winds
2264:
07 Shards and Shadows: The Greater Good
2267:
08 TOS Episode: Mirror, Mirror
09 The Sorrows of Empire [Pages 1-30]
2268:
10 The Sorrows of Empire [Pages 31-58]
11 TOS Episode: The Tholian Web
2269-2276:
12 The Sorrows of Empire [Pages 59-162]
2277-2295:
13 Shards and Shadows: The Black Flag
14 The Sorrows of Empire [Pages 163-449]
2333:
15 Shards and Shadows: Three
2344:
16 Shards and Shadows: The Traitor
2353:
17 Obsidian Alliances: Cutting Ties [Pages ??? - ???]
2354:
18 Obsidian Alliances: Cutting Ties [Pages ??? - ???]
2358:
19 Shards and Shadows: A Terrible Beauty [Pages 313-315]
2361:
20 Shards and Shadows: A Terrible Beauty [Pages 319-323]
2365:
21 Shards and Shadows: A Terrible Beauty [Pages 326-329]
2369:
22 Seven Deadly Sins: Lust: Freedom Angst
2370:
23 DS9 Episode: Crossover
2371:
24 DS9 Episode: Through the Looking Glass
25 Glass Empires: The Worst of Both Worlds
26 Shards and Shadows: The Sacred Chalice
27 Obsidian Alliances: The Mirror-Scaled Serpent
28 Shards and Shadows: Bitter Fruit
2372:
29 Shards and Shadows: A Terrible Beauty [Pages 335-340]
30 DS9 Episode: Shattered Mirror
31 Shards and Shadows: Family Matters
2374:
32 DS9 Episode: Resurrection
2375:
33 DS9 Episode: The Emperor's New Cloak
34 Shards and Shadows: A Terrible Beauty [Pages 344-351]
35 Obsidian Alliances: Cutting Ties [Pages ??? - ???]
36 Obsidian Alliances: Saturn's Children
2376:
37 Shards and Shadows: A Terrible Beauty [Pages 316-318, 323-326, 329-340-344, 352-358]
38 Shards and Shadows: Homecoming
39 New Frontier: Turnaround
40 Shards and Shadows: Empathy
41 Shards and Shadows: For Want of a Nail
42 DS9: Fragments and Omens
43 DS9: Olympus Descending
2377:
44 DS9: Warpath
45 DS9: Fearful Symmetry
46 DS9: The Soul Key
2378:
47 Rise Like Lions ?
I made this list awhile back and any mistakes are my own.