Learn Swedish: Jag kände på mig att något var fel. - I had a feeling that something was wrong.

The phrase känna på sig is a specific expression that means to have a gut feeling, to sense, or to suspect something. If you only used kände, it would mean you physically felt something or felt an emotion, whereas på mig adds that element of intuition.

Is på a particle here, and does that affect the word order?

Yes, känna på is a particle verb, and the reflexive pronoun mig comes right after it. In Swedish, the structure is verb + particle + reflexive pronoun, making it kände på mig. You cannot say kände mig på.

Why doesn't fel get a -t ending to match the neutral word något?

The word fel is an indeclinable adjective. This means it never changes form, regardless of whether it describes an en-word, an ett-word, or a plural noun. It always stays as fel.

Can I use någonting instead of något here?

Yes, något and någonting are interchangeable in this sentence. In casual speech, you will often hear them shortened to nåt or nånting.