や details

や

and — names a couple of nouns as samples and leaves the rest of the list unsaid

引ひき出だしには古ふるい写真しゃしんや手紙てがみが入はいっていました。

hikidashi ni wa furui shashin ya tegami ga haitte imashita.

The drawer had old photographs and letters in it. neutral

部屋へやにマンガやゲームが散ちらかってる。

heya ni manga ya geemu ga chirakatteru.

There's manga and games strewn all over the room. casual

Examples

and — two or more nouns given as examples of a longer list, with や between them and nothing marking where the list stops

引ひき出だしには古ふるい写真しゃしんや手紙てがみが入はいっていました。

hikidashi ni wa furui shashin ya tegami ga haitte imashita.

The drawer had old photographs and letters in it. neutral

部屋へやにマンガやゲームが散ちらかってる。

heya ni manga ya geemu ga chirakatteru.

There's manga and games strewn all over the room. casual

会議かいぎでは予算よさんや日程にっていや担当たんとうについて話はなしました。

kaigi de wa yosan ya nittei ya tantou ni tsuite hanashimashita.

At the meeting we talked about the budget, the schedule and who takes what on. neutral

パーティーには先生せんせいや学生がくせいが来きてたよ。

paatii ni wa sensei ya gakusei ga kiteta yo.

There were teachers and students at the party. casual

会場かいじょうへの飲食物いんしょくぶつや大おおきなお荷物にもつのお持もち込こみはご遠慮えんりょください。

kaijou e no inshokubutsu ya ookina o nimotsu no o mochikomi wa go enryo kudasai.

Please refrain from bringing food, drink or large bags into the venue. formal

面接めんせつには履歴書りれきしょや証明書しょうめいしょなどをお持もちください。

mensetsu ni wa rirekisho ya shoumeisho nado o o mochi kudasai.

Please bring things like your CV and your certificates to the interview. formal

The listing や joins NOUNS only and never ends a sentence — the last item
stands bare or takes など (パンや卵たまごなど). Actions list with
たり〜たり instead.

と
と claims the list is complete and や claims it is not — パンと牛乳ぎゅうにゅうを買かった says those two things were bought and nothing else, パンや牛乳ぎゅうにゅうを買かった says those are two of the things, so a receipt read out takes と and a vague account takes や.
とか
Same open list, different register — や belongs to writing and careful speech and sits between the items only, while とか is spoken and characteristically repeats on the items (パンとか卵たまごとか), so a notice takes や and a chat takes とか.
たり〜たりする
The same "some of the things, not all" claim on a different word class — や lists NOUNS (掃除そうじや洗濯せんたく), たり〜たり lists ACTIONS and has to end in する (掃除そうじしたり洗濯せんたくしたりする), so neither can take the other's host.
やら〜やら
やら lists too but adds exasperation and a refusal to be precise (書類しょるいやら印鑑いんかんやらで一日いちにちかかった), and it repeats on every item where や only sits between them.

など
や separates the samples and など closes them off, which is why the pair is one phrase (パンや卵たまごなど) — a list can close without など, but など can never start one.