Making lists with や, とか, など, と, か, and に

List of items in Japanese are made by tagging each item with a specific "listing" particle that defines the nature of the list. There can be both exhaustive and non-exhaustive lists. An exhaustive list is just a list that states explicitly every element it is comprised of. A non-exhaustive list is a list that provides a few examples or a description of the nature of its elements, while leaving space for ambiguity and indirectness.

"I went to the mall with Paul and Frank" is an exhaustive list, while "I went to the mall with Paul, Frank, and the rest of the crew" on the other hand is a non-exhaustive list.

Depending on the nature of the list, the final element often has its listing particle dropped and replaced with the case particle that applies to the entire list.

や makes a non-exhaustive list providing a few examples of elements that correlate to a general common idea of them.

スプーンやフォークで食べること
To eat with spoons and forks (and stuff like that)

と was covered as a side-note before, but here we'll cover it explicitly and compare it to や. と makes a "generic" exhaustive list. It counts every element in the list.

リンゴと魚とタイヤキ(と)を食べた
I ate taiyaki, fish, and apples.

As already mentioned, the last と is optional and usually dropped.

か can be used to provide alternatives. It is closer to “or” than “and” although the distinction is sometimes blurry.

スプーンかフォークで食べる。
To eat with a spoon or a fork.

とか makes a "vague" list. It's vague, and therefore non-exhaustive, but each item is its own. The items aren't necessarily considered to share a common property.

スプーンとかフォークで食べること
To eat with a spoon or fork (or something).

It can also be used to make things vague with just one element:

例えばデスクトップパソコンとか。
For example, (something like a) desktop PC...

To the surprise of no one, とか is basically like と + か. It can also be used to list verbs, often to provide alternative choices. This is a distinctive feature that doesn't exist for the other listing particles in this lesson.

戦えるとか戦えないとか、そういう問題じゃないんだ。
The problem isn't whether you can fight or not.

もしかして、付き合ってるとか？
Are you perhaps dating? (or something like that)

If the list is too long (more than 2-3 elements), it’s common to use commas to separate the elements in the middle without using particles.

など is not technically a listing particle, but rather some filler particle that sounds like using "etc" or “and such” in English. It implies the notion of a list of elements open to more similar stuff. Its meaning is similar to using a single や or とか to state that more examples are implied but not directly stated.

完璧な人間など、存在しない。
Things such as a perfect human don't exist.

These listing particles are also commonly used together, especially with など. The pattern Xや、Y、Zなど is incredibly common, like in the following sentence:

剣や斧、槍、弓など、様々な武器が置かれている。  
Swords, axes, spears, bows, and such a multitude of weapons were on display.

There is another listing particle that is sometimes overlooked: に. This particle is used to list things that come together in a set, or that the speaker is listing one-by-one as some form of chain of thought or active recollection.

サンドイッチにミルクにコーヒー。
Sandwiches... milk... and then coffee.