"Could" and "might" can be used interchangeably. Since you gave specific examples, I'll give you specific connotations: "I could work harder" suggests that if they paid you more, you would somehow be better *able* to work, as if something about your current pay level were making it impossible for you to work harder. "I might work harder" does not specifically refer to your ability, rather, it just talks about something that might or might not result if you were paid more. "I would work harder" is another option in the 3rd conditional, which in this context would suggest that you're not currently working as hard as you could, because you don't want to. Actually, whether you use "could," "might," or "would," it would appear that you're not currently working up to your potential because you think you deserve higher compensation. Good luck getting that raise!

Yes, 'might' and 'could' have the same meaning and can be used interchangeably. Sometimes they can have different connotations. For example, using 'might' in the first sentence has a connotation that you may or may not work harder if they pay you more. Using 'could' makes the second sentence have the connotation that you will be able to work harder because they pay you more. But both 'might' and 'could' express in the sentence what you will possibly do if you get paid more.

Personally, I think the biggest different between them is amount of emphasize on willingness of the subject. It means 'could' illustrate the possibility of subject's willingness.