I know they can all be translated as something, and I know that что-то differs from что-нибудь in that it refers to something concrete, but not mentioned (whereas the former refers to anything at all) - but that's all I know.
что-то would be normally used when the speaker has no knowledge of what the object is, e.g.:
кажется, я что-то вижу - I think I see something
что-то не так - something is not right
что-нибудь would be used to name one unknown item that belongs to a category/set:
дай мне что-нибудь [выпить] - give me something [to drink] - from a set of drinks
что-нибудь also replaces что-то in questions:
- Ты что-нибудь видишь? - Do you see anything?
- Да, что-то вижу - Yes, I see something
кое-что is generally synonymous to что-то, but can be used to express eagerness on the part of the speaker:
- У меня кое-что для тебя есть! - I have something for you!
нечто is a deprecated form of что-то, but now has an additional meaning of surprise/excitement, in this meaning it can be translated as thing:
- Это нечто удивительное! - This is [something] wonderful! / This is a wonderful thing!
- Он просто нечто - He's just so cool/great (colloquial)
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6Usually, 'кое-что' implies that: (1) the speaker knows certainly for what it stands (usage of 'что-то' may mean that the speaker is uncertain); (2) the speaker is withholding this information. For example: 'Приходи к нему в гости, у него будет кое-что вкусное!' - 'Come visit him, there will be something delicious! [I know what it is, but won't tell]'. 'Приходи к нему в гости, у него будет что-то вкусное!' - 'Come visit him, there will be something delicious! [He said so, I don't know the particulars]'.– achJun 15 '14 at 13:53
Что-то = simply "something"
I spotted something.
Нечто = something in bold. Something surprising, unexpected, stunning.
I spotted something.
Кое-что = something I know what but will not say.
I spotted something, but this is secret.
