Back in the 80s I had a box of Speer 150 gr. full metal jacket Lawman ammo. It was .38 Special +P.
I've never seen the .357 FMJ +P, so I can only comment on the .38 Special +P I shot long ago:
Good stuff. Loaded rather hot. I wouldn't use this in anything less than a K-frame Smith & Wesson. It might strain the little J-framed snubnoses.
As I recall, it was quite accurate. It seemed to shoot to same point of aim as my practice loads, which used a 158 gr. lead semiwadcutter over Unique or Bullseye, for about 850 fps.
Perhaps it shot a little lower. I'm trying to recall but it's been at least 25 years since I shot it.
The .38+P FMJ would be good ammo if you were in the military and HAD to use full metal jacket ammo. It might be useful to knock off grouse or rabbits without ruining a lot of meat, but it's noisy.
For this application, you'd do better to shoot lead roundnosed ammo or the current 130 gr. full metal jacket ammo, which is rather weak; about 800 fps from a 4-inch barrel.
If you've stored it in a place without temperature extremes, it should not be deteriorated.
It would be useful ammo in a K-frame if you had to engage barricaded bad men, such as crooks in cars.
I don't know what the .357 Magnum is loaded like, but the .38 stuff was skookum stuff.
If you have a full box, offer it to a cartridge collector. I suspect it's not common and might fetch a little extra than regular .357 ammo.
Then take that money and buy some regular .357 Magnum ammo.
It would be a shame to shoot up such unusual ammo.