Which one is right — "He works at company X" or "in company X "?

I usually use "at a company" but I have encountered some articles using "in a company", "in XYZ firm" or "in an organization".

Which one is right?

Use:

I work in/at/for a company that makes microchips.

I work at/for Intel.

I work in/for Intel's accounting division. (in sounds more natural in this case)

There is virtually no difference in meaning, except that I would notice:

• for tends to emphasize the relationship you have as an employee to your employer

• in / at are more about the physical place (this is where you go to work every day)

• I work at Avaya. — YEAH
• I work for Avaya — YEAH
• I'm with Avaya — YEAH
• *I work in Avaya? — NOPE

Edit: "I work with Avaya" is more likely to mean you aren't an employee but may be an independent contractor of some kind.

Thanks @Robusto for the insights!