Most of those items fit the 200 series, up through your 340. There was no 360, other than an engine. You can do Google image search for a IH 340, and compare physical characteristics, and see if they compare. The 240's 340's, 460's etc, were the first generation of the square front grill. The series before that were rounded like the older farmall's.
If it is indeed a 340. it will have the C-135 engine. Should have a 5 spd. forward transmission, 1 reverse.
You can go to Case IH:
Case IH Agriculture Equipment & Farm Tractors
and compare part numbers on castings, etc.
If you click on that link, when the page opens, select "parts & service" in the menu at the top.
Next page, scroll down to "search for genuine case ih original parts" In red, you will see "search for parts". Click on that.
Next page that appears, enter you model number, and it will have a menu appear to select your particular tractor. Utility, Farmall, gas, diesel, etc...
Next will appear a selection of components of your tractor. Select what you want to see, and it will have an exploded view of it. Below are part numbers.
For engine parts, you will need to go back to the model number selection, and type in C-135.
Usually at the very top of component listings, it will say General. Click on that, and it has general info such as, where to look for the serial # locations, on the chassis, and engine, and also has a view looking at the tractor from the right front.
Hope this helps a little..!!