We have a traditional New Year's Food called "Oosechi" in Japan. We have a traditional New Year's Food called "osechi" in Japan.

We have a traditional New Year's Food(food / dish / food item) called "Osechi" in Japan. We have a traditional New Year's (food / dish / food item) called "Osechi" in Japan.

I buy Oosechi at a supermarket every year. I buy osechi at a supermarket every year.

I buy Osechi at a supermarket every year. I buy Osechi at a supermarket every year.

If you always go to the same one, it might be more natural to use "the supermarket". If you say "a supermarket" it gives the idea that you might go to different ones each year

This year, I bought a three layer boxes of Oosechi. This year, I bought a three layer box of osechi.

One single 3-layer box? Or 3 layers as in a stack or pile of boxes?

This year, I bought a three layer boxes of Oseboxes of Osechi with three layers eachi. This year, I bought boxes of Osechi with three layers each.

When talking about a plural noun, eg: "boxes", I feel like it's most natural to use a relative clause after the noun

This year, I bought a three layer boxes of Osechi. This year, I bought three layer boxes of Osechi.

"a" is for singular object, but "boxes" is plural.

There were many kinds of dishes in each box, and each dish was put in a small container. There were many kinds of dish in each box, and each dish was put in a small container.

When using "kinds of" what follows is singular.

Most of them are traditional old fashioned foods that have been passed down for a long time, but some of them are really tasty. Most of them are traditional old fashioned foods that have been passed down for a long time, but some of them are really tasty.

Most of them awere traditional old -fashioned foods that have been passed down for a long time, but some of them are really tasty. Most of them were traditional old-fashioned foods that have been passed down for a long time, but some of them are really tasty.

The plural of food is foods. It's a little odd, so might not be immediately obvious when to talk about food (collective) or multiple distinct foods. If you're talking about in general, use "food", but if you are talking about multiple kinds of food (like here), then "foods" is appropriate

Most of them are traditional old fashioned food thatwhere the recipes have been passed down for a long time, but some of them are really tasty. Most of them are traditional old fashioned food where the recipes have been passed down for a long time, but some of them are really tasty.

You can't actually pass down the food itself (that gives people the impression of "Here is my grandmother's old baguette" and handing someone some moldy bread), but you can pass down e.g. the recipes.

Those New Year's Ffoods are called Oosechi. Those New Year's foods are called osechi.

Those New Year's Ffoods are called Osechi. Those New Year's foods are called Osechi.

Thoese New Year's Foodmeals are called Osechi. These New Year's meals are called Osechi.