So I have killed a couple dragons now and have been holding on to there bones and such for dragon armor. But because the whiegh a ton I am constantly have to drop other expensive gear just so I can finish a dungeon and move on. Where am I able to store my gear till such time as I need them

Buy a house and put it in chests

get a companion and use them a a mule

yes but anywhere I am able to put it before buying a house

I am saving the 5k for a house, I only need about 500 gold now, which should be any moment.

For now I've been using Lydia and a couple of barrels in the Companion's meadhall. So far the barrels have held all my items. I've also heard you can use the dragon skeletons to store things in, but they move around for me and I worry they may bug out.

I believe someone made a thread about this yesterday and said it worked fine to put your stuff in random barrels or whatever you can find, I wouldn't recommend it though.

Do not store your gear in dragon skeletons! They disappear.

I bought the house in whiterun asap cause I knew I would have to store nice things, as soon as I finished the intro I chopped 7000 gold at riverwood so I could buy the house in whiterun and all its furnishings.

Pete said you can only store your gear in "owned" places. It's not safe to put it anywhere else. It was my personal quest to get a house as soon as I could and I just now got one at Level 10. It makes a lot of difference. Now I can head out and travel light and have Lydia able to carry more.

In the mean time, there are some tricks when you're holding too many items to getting around. Sometimes if I am way past my limit but have some great items to vendor I use them. You can ride on your horse as fast as you normally could no matter how much you're carrying, and there seems to be a bug where even though you can't fast travel when you're holding too many items, you can get on your horse and then select fast travel and it works. I personally avoid fast travel for immersion purposes but I know it's possible.