Depends on which timeline Q pulls them from, the one where Lucas has it satisfyingly vague in a zen mysticism sort of way, or the one where Lucas has two decades to think about how to screw up what he made and gets irritatingly specific. Obi Wan McGuinnes describing it as an energy field or the one with Qwi Gon Neeson prattling about midichlorians?
The movies, and therefore canon, suggest that the force can be localized in strength or composition, which supports the expanded universe which contains locations and people which are dead to the force, locations in which Jedi cannot access the force and races which are "force immune." This suggests that a handful of Jedi who were bamfed into the ST universe would find themselves cut off from the force, and would likely lop off their own toes the moment they activated their lightsaber.
Or Q could just be like "**** it, it was funny to have Picard meet Xavier, midichlorians for everybody!"
Final result: "Sorry, Troi, we're all empaths now, go crash a different starship."
The Federation will quickly attempt to locate those with force powers and control them thus making the Federation "the Empire", the Romulans and Klingons will try to subdue the force weilders but learn that they can't, and join them in their epic war against the empire. The borg will simply be taken over by the mind control powers in force weilders and also aid in the struggle against the oppressive imperial forces.
lordmalak1 that sounds more like something the mirror universe would do, and in that case it wouldn't be Jedis but Sith in stead. lol As far as the origin 5 getting beamed on the enterprise and tossed in the brig. I don't see that happening so easy. With all their powers, that might be a very bad move on there part. Plus the fact Q might hide them from Picard in the 1st place, so he can effect the timeline to see what happens.
I can see 1 or 2 new Jedis being part of a Captain Archer's crew, and helping to keep that crew safe. Maybe they would find more new Jedis along the way, or even new Sith that are spawned from these other worlds.
Knowing Cryptic, there'd be Jedi officers and Sith fighter pets. The player would encounter the force in friendly and non-friendly ways, as follows:
Player approaches an enemy ship. At a range of 10 km, the player moves his mouse over the skill bar or tries to press his skill hotbar key. A dialogue box appears:
Tactical Officer Jinn Gon Qui: All abilities mapped to 'Z' on the keyboard have been activated. May the force be with you.
The player is fighting an enemy ship and the hull strength is down to 25%. The player wants to repair his hull and moves to click on or press the hotkey activating engineering skills.
Engineering Officer Kinobi Wan Obi: All engineering abilities have been continuously activated ever since the battle began. They are currently on cooldown. May the force screw with you.
The Sith Fighter pets would be totally independent and single minded. When the carrier orders attack / retreat patterns, the result could be friendly or unfriendly.
FRIENDLY RESULT: Fighter Sidius the Darth: They shall be melted into lava and blown to bits before your royal dark posterior! We shall bend the Pe'taqs! Join the Dark Side today. Call 1800...
UNFRIENDLY RESULT: Fighter Tine Palpa: Retreat? Do you follow the semi-darkside of the force? What the hell is RETREAT? Charge! Throw our lives away in sheer folly! To hell with living! Q'apla!
The C-Store and Cryptic Devs would also be transformed, thanks to prolonged exposure to the force. This will result in positive and negative effects.
POSITIVE EFFECTS: Master Yoda Stahl.D: The force is in the Defense Force unbalanced. Ensure the creation of content timely and satisfy the players we shall. Balance shall we restore. May the force our creativity power!
NEGATIVE EFFECTS: Mistress Darth Investor: How can we justify not milking juicy wallets? RAISE THE COSTS! Put ALL the ships in LOCKBOXES... EXPENSIVE LOCKBOXES! MORE ZEN SALES! MORE MORE!
C-STORE ADD-ONS: 1. Ferengi Bargain Mind Bender: With a 1 hr cooldown, this handy item will convince exchange shoppers that your items are priced as 1 EC each and will rip them off for 1 Billion EC, when they buy the item. If they don't have that much EC on them, it'll give you a mortgage over their ship, until they pay off the ECs in instalments, with interest.
2. Undine Psyonic Force Throw: Fixed in the garbage recycler slot of your tactical escort, this unique force device will allow you to throw items from the Gamma quadrant to the Alpha quadrant. Why that source and that destination? Ask the Force. Accuracy is not guaranteed, although this console does carry CritDx5 and CritHx10 modifiers.
3. Ablative Thought Powered Armor: Equipped in Turret and Cannon slots, this console provides 100% resistance to kinetic and all energy damage. However, it requires that you equip the console in ALL WEAPON SLOTS. Pacifists and spiritual aspirants are ideal buyers.
4. Credit Card Usage Console: Automatically buys zenny for you, without your knowledge, using your retirement savings. The Force will mimic your voice for telephone banking, your password and username for internet banking, and create a powerful duplicate, who will sign your cheques and demand drafts in your name. The duplicate will not, however, act for you in the bedroom. Not refundable and cannot be deactivated, once it is used.
Such is the consequence of two dimensions mingling. Down this path, one walks only once, for there is no return.
AvP is the only time I want to see genres merge and even then the movies sucked, Jedi's in Star Trek?, no, No, evil, kill it, kill it with fire.
In Star Trek faster than light travel and artificial intelligence is still a growing technology and has only been available for a few centuries, in Star Wars the technology has plateaued and has been commonplace for millennia.
Star Trek has subspace, Star Wars has hyperspace
Star Trek has transporters, Star Wars has lots of robots
The genres are just too different
Star trek already has races with psionic abilities, we don't need psychic warrior priests wandering around.