I know in the second conditional there is an exception about the first person.
For example: if I were (not was) you, I'd buy a new computer.
What about the third person? Should I use: If he were you... or If he was you?
If he were you...
Yes, in order to put a clause in the so-called subjunctive mood you theoretically should use were with third-person singular subjects like "he, she, it". Wikipedia calls such constructions past subjunctive:
The main use of the past subjunctive form is in counterfactual if-clauses:
If I were a badger, I would choose that color.
He would let us know if he were planning to arrive late.
Quirk et al. also conveniently call this construction were-subjunctive.
In the overwhelming majority of non-formal cases, it won't be a big deal if you don't use were in such construction, though. You can use was, it will be considered slightly less formal, but acceptable. But see the P.S. section below concerning the expression "if he were you".
According to Quirk et al.,
In nonformal styles, hypothetical past or indicative forms replace subjunctive were:
1. I wish she was not married
2. If only I was not so nervous
3. Suppose he was / is lost, what would you do?
P.S. Quirk et al. remark that in the fixed phrase "If I were you" the form were is still considered normal (at least it was in 1985, when the book was printed), so I guess it's better to use were in this phrase. They also note that in the fixed phrase "as it were" the form were cannot be replaced by was.
So it appears there are bastions where were is holding fast, like formal/fixed/often used expressions and there are areas where you can give yourself more freedom.
Reference: Quirk et al., A Comprehensive Grammar of the English Language, Ch. 3.62, "The were-subjunctive", and Ch. 14.24, "The present and past subjunctive".
If I was back at home right now, I'd be eating my wife's lasagna.
If Barbara was any taller, she'd be too big for the car
If I were back at home right now, I'd be eating my wife's lasagna.
If Barbara were taller, she'd be too big for the car!
In old-fashioned, prescriptive grammars, people used to say that we should always use were in these types of conditional, for both first and third person singular, as in examples (3) and (4).
However, we now know that this is not a grammar rule of English. It is not even a good style rule. The best and most famous writers in English have always used both was and were for the first and third persons, as in examples (1) and (2).
There are, however, some fixed phrases where writers have consistently used were. The best known example is in the fixed phrase:
However, in actual speech, not writing, If I was you is actually extremely common. It is only in written English that we almost exclusively use were in this phrase.
Hope this is helpful!