Ok, didn't read the victory conditions. I didn't realize you needed 150. Having to make up 150 to get a win would be tough. 30 would be very doable.
1) Plasma I think we both agree would slaughter Gorn in corner.
2) Kzinti can get 24+ drones in the air with a typical 450 pt force. That should tie up the Gorn phasers at the very least. 3 ships can typically do 2-3 burnthrough in all except turn 1 on average since each ship probably has 4 dis and 4-6 PH1 which averages over 10 pts of damage at range 15. So you should be able to inflict 10-15 internals over the course of 6 turns just on burnthroughs which should be faster than he can repair. If you reach range 10, you can target weapons to make his repair more difficult. On turns where the drone wave hits, the 3rd Kzinti ship that's not targetted by plasma can get the range 8 shot and inflict even more damage.
However if you concentrate on 1 ship, you can get better results. His small ships are HDDs which have 3 batteries each, so he can block 9 per turn from 3 ships. Your ships do 12-14 on average at range 15, leaving 9-11 damage net per ship, even more for a ship that reaches range 8. 3 ships would do in the high 20's of net damage per turn from turns 2-6. I don't think a HDD can stand up to this punishment even if he constantly rotates shields. Other than his 1 shield, he only has 24 shields in each direction and eventually the damage will start degrading his ability to defend drones and maintain a plasma threat against a close approach.
3) Klingons would have to follow Kzinti strategy except they have fewer drones and thus might not risk 1 ship at range 8 since the Gorn might be able to fire back effectively.
4) Lyrans/Selts have more PH-1 so a higher net damage per round. A Lyran force at range 15 can average 14-16 per volley or 11-13 net after batteries to a HDD. A Selt force of DNL and 2 NCA has an astounding 11 PC and 30 PH-1. The HDD is completely toast over several turns.
5) ISC would have an easy time. Their fleet would hae 3-4 PPD plus plasma. Even without plasma, 3-4 PPD and about 20 PH1 should be able to damage a Gorn fleet at range 15 enough to win. With plasma, it's a cakewalk. IMO, they have the best chance at the 150 pt victory condition.
6) A Hellbore fleet likely has 12 HB, or 36 shots over 6 turns plus lots of misc PH shots. I can't see a HDD stand up to that kind of punishment.
7) The most likely Andro fleet is Int + 2 Cob. What they can do is to use a displacement attempt at Gorn ships and hope to draw it out of the corner by a decent number of hexes. If that succeeds, they should be able to inflict enough damage to win. It helps that the Int has 2 DDs, but there are only 2 directions that benefit the Andro for the displacement attempt.

Fed/Vudar have to get lucky with a range 8 shot. They tend to have lots of PH-1 to chew up Plasma, so they might be able to get to range 8 and unload Phot/IC without taking significant internals.
Bottom line, they might not get a win, but they can assuredly give the opponent a loss. And 20 turns seems like an unbelievably long time to defend against my Cat 2 fleets.