I need to install a new cord on a curing oven I purchased for the shop. Does it matter which prongs I attach the black and white wires to? I know the green wire has to be attached to the ground prong.

green to ground.
white (N, neutral) to the wider blade on the plug.
black (L1, hot) to the narrower blade on the plug.

ar-jedi

ps:
always remember, in US residential wiring, BLACK = DEATH.

It's 220v that I'm wiring. There aren't two vertical blades. There is 1 horizontal, 1 vertical, and 1 ground. I should had mentioned this in the original post.

ya think?

that is not a 240V plug you show, by the way.  
above is a NEMA 5-20P, which is designed for 120V 20A.  it mates with the NEMA 5-20R receptacle shown below.

please post the correct 240V plug you have.  in any case, it doesn't matter here.  in a split phase residential system, you get 240V from the combination of the two phases.  so, with a three-wire plug as you describe (G, L1, L2) –– you can wire black and white to either of the two blades, as they are both live.  

nevertheless, i have covered all possible scenarios with the image below.  

ar-jedi

Here's a pic of my 220v outlet and the 2 plugs I will be using with it. Both plugs say 250v 20 amp, are these safe to use with my outlet?

that isn't the same as the plug you posted in the first place.  
compare carefully, you'll see the difference.

in the post directly above:
–– top is a NEMA 6-20R receptacle.
–– bottom is a NEMA 6-20P plug.  
they are 240V 20A.  
you are good to go.

it won't matter which blade you attach the black/white wires to.  
wire it up and go to work.

ar-jedi

I notice that now.