Realized this at the end, put it here bc it's prob the most useful advice. There's a twitch guy who may or may not have the best commentary but plays a decent amount of Olaf at really high level http://secure.twitch.tv/hashinshin/profile/past_broadcasts and you can watch his past broadcasts so you don't have to make sure you catch him streaming (sept 11 one is olaf in the title). Watch some of his olaf games and look at what he's doing that you're not and try to pick one thing to work on each game until you get better at that thing (ie how you path to pick up axes in fights, or timing your steroid which I am forgetting the button of :P), that's what I did w/ heimer. Learning how phasekiller (challenger kr heimer) used level 6 ult turret to make early tower dives happen was a huge boost to my laning in bronze, so was learning to auto attack harass more.
So it may be an experience thing, but the amount you're dying you're not judging damage right, or if you are then you're losing so hard you can't really fight and should try to get back in other ways. If you're even or winning lane it is almost impossible to die to a tower dive (and not go 1 for 1 or 2 for 1 if you're lucky, assuming you do die) unless you misplay it or don't understand the match up. For instance a number of champions that heimer matches up against require that heimer takes exhaust or he WILL lose the lane assuming equal skill of each player, and if you're going to spam olaf you should know those match ups.
Most importantly though I'd say there are two things that jump out to me as easy to suggest help on, and one that I can point you in the right direction but would have to watch game play to give advice on how to fix.
The first is that you do seriously need to work on CSing. Play something like nasus that just hyper focuses on farming for like 10 to 20 games if you can't find any other way to focus on improving it, but you can look at your cs@10 minutes on op.gg if you click the magnifying glass on a match history and then hit the cs@10 tab by the bottom. Yours is here http://na.op.gg/summoner/userName=jotunhelm and in a god game you're around 50 ish, but more often you're in the 40 range and a bad game you're in the 30s. A kill is about 15 cs, so if you are at 60 cs instead of 30 cs, then it is like getting 2 free kills. If you're 2-0 and 30 cs but your opponent is 0-2 but 70 cs, you are losing lane. The little number in parenthesis next to your cs total is your cs per minute, and my good jungle games hit around your average game. I played high farm champs and there's a big difference between high bronze/low silver and high silver/low gold, but your average cs per minute is around 4 (5 something on a good game), and when I laned I had 6-7 cs per minute on a decent game and 8 or 9 if I had a really good farm game. Imagine what an advantage the difference between 6 cs per minute and 4 is. At 10 minutes (so 12 in game bc minions don't spawn immediately) that's a 50% bonus in gold for the first person. If each cs is 20 gold then 40 cs is 800 gold and 60 cs is 12 gold. That's a huge difference in item buys if both people back at that mark. It will take time, but I noticed when I started farming better games became easier bc I was ahead instead of behind when we both came back to lane after our first buy.
Second, take tp top. It's not something you always have to do, but especially if you're struggling in lane it is a god send. You can start raptors easy w/ Olaf, just undertow and auto while picking up axes and spamming undertow. You'll get level 2 and some gold and then back to buy, and tp up top when your hp is like 3/4 if I remember right (I know looking at my screen but not sure the exact number bc it's just habit at this point how much hp I need to regen before I can tp and the rest will regen before the tp finishes). Then you hit lane at level 2 w/ 2 spells, and more sustain bc you have your starting item (doran's blade, doran's shield, flask, ruby crystal, whatever) plus the extra gold from killing raptors so you then have like d blade 5 hp pots 2 mana pots, or like cloth armor (buy it by itself, kill raptors and back) and flask which you have just enough for if you don't buy pots w/ cloth armor to kill raptors (or you can buy flask solo, back and buy cloth armor for lane, either way). It's a big advantage in early lane phase (especially the level advantage) and it lets you tp bot if there's a big bot lane fight that you could clean up kills in, or tp back to lane if you get shoved out by a gank or something.
Third is find out why you're dying so much and try not to do it so much. Oddly enough in my experience higher rank isn't so much about being able to kill people more, but about being able to die less. The enemy team (especially you lane opponent) gets less gold if they don't kill you, and you can build the gold advantage through farm if you aren't able to kill your opponent bc you don't want to dive and die trying to kill them or whatever. It's hard to say what it is that helps you not die, but that's the simplest explanation to it. Whether it is learning to think like mid/jg and know when you would be roaming to gank you (so you can play safe/ward then) instead of just warding w/out thinking, or learning when to let a kill go and stop chasing bc you don't have vision or whatever, or just learning how to kite better under tower and let the tower do more damage to the enemy while you avoid dying instead of worrying about killing them, whatever it is just find something and improve on it so you die less.
I'm not sure if that was useful, but I promise if you can find a way to get up to higher cs numbers (if you can't do it on olaf you may want to look at why, and if a different champ would be easier for you to play), and die less than you will go up in rank no problem. TP should help you a little w/ both honestly bc it means less time not in lane (so more cs) and it means higher exp so you aren't as easy to pick on if they're trying to kill you.