Learn Swedish: Ingen köper sådana kläder!

Because sådana is the plural form, and it must agree with the plural noun kläder (clothes). If you were talking about a singular en-word, you would use sådan, and for a singular ett-word, you would use sådant.

I often hear Swedes say something that sounds like sånna. Is that related to sådana?

Yes, they are exactly the same! In everyday spoken Swedish, sådana is almost always pronounced as sånna. The singular forms get shortened in speech too: sådan becomes sån and sådant becomes sånt.

Why is it kläder (indefinite) instead of kläderna (definite)?

Words like sådana (such) are followed by the indefinite form of the noun. This matches English perfectly, where we say 'such clothes' rather than 'such the clothes'.

How would I make this sentence singular if I meant 'Nobody buys such a piece of clothing'?

The word kläder is always plural. To talk about a single item, you need the word ett klädesplagg (a piece of clothing). Because it is an ett-word, the sentence would change to use the singular ett-word pronoun: Ingen köper ett sådant klädesplagg!