JLPT N3. Informal—used only in conversation.
なんか and なんて are heard
1. Emphasis
今日はなんか暑いよね。
Today is so hot.
今日はなんて暑い日だよね。
Today is such a hot day.
なんかきれいだ。
なんてきれいな部屋だ。
What a beautiful room!
They mean the same thing, but なんて is used when a noun follows.
2. Express disbelief at a situation or the prospect of something.
なんか takes the place of the particle; whereas なんて has the ability to nominalise the preceding verb.
お母さんが酔っ払っているなんて見たことない。
I’ve never seen my mother drunk.
大達さんが会社に遅刻するなんて珍しい。
Otatsu-san late for work—that’s rare!
自分のせいじゃないんだから謝る必要なんかないよ。
It’s not your fault so there’s absolutely no need to apologise.
なんか here is used to express that the idea of apologizing would be unbelievable.
僕にとって智子が大切な友達だけど、それ以上の気持ちなんか考えられない。
To me Tomoko is an important friend, but I couldn’t think of feeling above that.
3. To soften a suggestion. This is a rarer usage of なんか.
今週の日曜はドライブなんかいかがでしょうか？
This weekend, how about going for a drive?
This usage is related to (2) above in the sense that you are indirectly assuming the suggestion is far-fetched (or slightly unbelievable) but want to suggest it anyway.