ノー残業デーって英語でなんて言うの？

This means that there is no overtime on this day. You can even give it a fancy name like "No Overtime Wednesday".

"There's no overtime allowed at my office on Wednesday."

This is the way you would express that your office doesn't allow employees to work overtime on Wednesday.

You: "There's no overtime allowed at my office on Wednesday."
Person: "It must be great to have some time off!"



"There's no overtime today."

This is a way to tell someone that you are not working overtime today.

You: "There's no overtime today."
Person: "That's great! Why don't we do something after work?"



"In Japan, we sometimes have days where overtime is disallowed to prevent overworking employees"

This is a way you could tell someone who is not familiar with Japanese work culture that there are laws to prevent too much overtime, while also explaining to them that too much overtime is very common.

You: "In Japan, we sometimes have days where overtime is disallowed to prevent overworking employees"
Person: "Thanks for the information! I didn't know that."

In the UK this would probably be explained by saying something like:
"Wednesdays are overtime-free days."
However, what is more important is why these days are free of overtime? Was iot a management decision - or perhaps a union decision? In the UK such comment would immediately give rise to the question: "Why?'
"Wednesdays are always overtime-free because the workers union forced the company to ban overtime on Wednesdays."

overtime pay - this is the pay you get for working more than 40 hrs/week and usually the rate is 1.5 times the normal working rate

We aren't allowed to work extra hours on Wednesday's to prevent workers from getting overtime. - "to get overtime" means that you are paid for some overtime work, so you are getting 1.5 your normal rate for those extra hours

Some companies do have policies regarding overtime. One of the policies may prevent doing overtime on certain days or after a certain hour. In this case, overtime is not allowed on Wednesdays. There may be another policy preventing workers from doing overtime without authority.
So, you may say:
We don't allow overtime work on Wednesdays.
or
Wednesdays are overtime free days at our company








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It would appear that this is a kind of" a cost saving exercise "... and a way to make sure this company does not run out of " cash flow". 
"It's part of the company's policy; wednesday is an over-time free day."