a) In the Radio Drama, Luke wows everyone on the simulator, so he gets put in charge of Biggs and Wedge. Which doesn't make too much sense; just because you're good at your job doesn't mean you're good at leading other people in their jobs. Luke's experience blowing up womp rats might make him a fine pilot, but it doesn't mean he'd be good at commanding other people and leading an attack. Although Luke does seem to know what he's doing when things get hot.
b) There's a cut scene (maybe uncut in the SE, who knows) in which Red Leader talks about Anakin Skywalker and what a great pilot he was. If you smash your head into a wall a few times, it makes sense that Red Leader would promote Luke because of his father.
c) Either of the above, combined with Biggs's remark that Luke was the best bush pilot in the Outer Rim. Biggs is an Academy graduate, so he has at least some say-so. Though I'm not entirely sure why he'd want to subordinate himself to Luke. Even in all the cut scenes between Luke and Biggs, it's obvious who's the alpha dog, and it's not Luke.
d) Leia pulled some strings. She was probably the moral and financial backer of the Yavin Rebel cell, and for whatever reason she decided Luke should be boss of a couple people. Chalk it up to "Force impressions" or that wonderful sibling lust they had going for them.
As for Wedge replacing Han in the trench attack, I'm all for it. It's always bothered me how Solo, unprovoked, fires on Vader. It makes him seem like a murdering pirate instead of the patient, tolerant, friendly hero that he is.