Most of this comes from MMR. Normal games also have a type of MMR that matches you with players according to raw skill and less based off of ranked stats.
EDIT: "Raw skill" was bad word choice, I cite a post acknowledging the existence and function of hidden Normal MMR and explain in general how it works. This is all in a post below.
EDIT2: Re-posting my below explanation in case any confirmation/criticism is in order.
http://forums.na.leagueoflegends.com/board/showthread.php?p=27113153#27113153%3Cbr%20/%3E
(Scroll down a little bit so see the red response, it doesnt address the issue directly, but proves normal mmr exists)
Raw skill was probably a bad way to word my answer and I apologize. I will supply you with a post about MMR scaling, but it does not directly answer, your question, i need to search deeper for that post. I believe Zileas replies to a summoners concerns over why Normal MMR is hidden, which pertains to the topic of why your are teamed up with such varying players due to the fact it acknowledges Normal MMR and its function. Your awkward placement seems to stem from the hidden Normal MMR. This MMR calculates like ranked MMR, but for many summoners who play mostly ranked and only on occasion play normals, there are large gaps between ranks and match placement. For example, lets assume I am a diamond player who only plays normals once a week. If I tend to lay back and play loosely, trying new champs and build or just plain out trolling, my MMR will be low naturally. Some players don't like the stress brought upon by ranked and dont play it, but do fabulously in normal games. These players can have a bronze ranking but high MMR in normal due to their preformance