You need to use a trainer or you need to edit a savegame to unlock wide body kits for all cars in your garage. Note that there are no wide body kits for the SUVs.
I think I unlocked the widebody kits for all cars in my career garage in this zip of savegames (meant for the US version of U2):
In these savegames, all cars (my cars and career cars) have all performance uniques installed, and the ecu/turbo tuned by editting the savegames for optimal peformance. The only exception is the 240SX and RX7, which have all but the unique tranny, which slows them down in drag mode. I have 2 RX8's, RX8 #1 has all uniques but tranny, RX8 #2 has all uniques.
Some players stated that the wide body kits actually made the cars wider for game play, which impacts lap times because you have to turn more to avoid hitting walls, or the widebody kits made the cars more prone to crashing if you bounced or slid along walls. I was never sure of this, but I did remove wide body kits on the cars I used for online racing. I left the wide bodky kits enabled, so you can reinstall them if you want to use them.
In addition to the wide body kits, 5 of the unique vinyls are normally one career car only if you don't use a trainer or edit a savegame. This is a list of those vinyls and the internal game code for them:
octo - 1ac758bd
fish frog - 9fcc3041
eyepile - 957778d9
drag-sect - 990fa607
evil eye - ca4ad5a4
Unique parts like split hoods (trap) and split spoilers also require editing savegame or a trainer to unlock for all cars in career garage.
Off topic, but stage 5 is the west part of Coal Harbor.