Major garden overhaul

The second picture is what my perennial garden looked like when we first moved into this house about 3 months ago.
The first picture is what it looks like now after I cleaned it up, gave it some much needed care and water and sat back and patiently waited to see what bloomed. It is clearly so overgrown and looks horrible! I am planning to rototill it in a couple of months. There are quite a few flowers in there that I'd like to dig up and replant though. Here is a short list of some of them that I can identify:

Jonquils, Primrose, Irises, Mullein, Hyacinths, Poppies, Bellflower, Sedum, Mums, Coreopsis, Hydrangea and Achillea.

There are also a million strawberries growing in there that I am just going to get rid of as they are taking over the bed and the squirrels eat them anyways. My question is though....does anyone have any advise on digging any of these plants up and replanting them? I've never done a complete overhaul like this so any advise you have would be greatly appreciated!

My poor Coneflowers!

Pretty? Yes, now look at the picture below :-(
The flowers look wonderful but then when you look at the second picture you can see how they are completely growing sideways...they are almost laying on the ground, so sad cuz they are such a beautiful flower. I just inherited all of these flower beds (we just moved in) a few months ago so I'm still on trial and error....do they need to be moved? They are planted in mostly shade and they are on a small slope...perhaps that is the problem?

Strange viney thing....??

This vine is planted on the side of our garage and it has gotten HUGE! I have no idea what it is but it grows out and some of the vines reach the ground and actually grow out from there also.....anyone have any idea what this is?

Peonies

well I thought my Peonies were going to do good this year but I only got a couple of blooms from them. They started off looking really good then we had a pesticide company come over and spray for bee's and spiders. I wonder if this chased all the ants off that fertilize them? After they sprayed I found very few ants on them. Also the trees overhead have grown out of control....maybe they just didn't get enough sun?

Hosta arrangement

I read an article in my Martha Stewarts Living magazine about how to make flower arrangements with Hostas and I thought...thats really a great idea because Hostas don't really put on a great display in your garden. So anyways, I gave it a shot and here is the arrangement I came up with! I love it and have gotten numerous compliments on it. I just put about 5 big Hosta leaves in the vase, put a few Iris folliage (leaves) in between it then stuck just a couple of perennials in the middle to give it some color. It has been on my dinning room table for 6 days now and is just starting to wilt a little bit, so it made a great centerpiece for almost a week now! Try it out and send me your pictures, I'd love to see them!

White flowers

These look like some sort of lilly? Folliage at the bottom then the flowers shoot up on long stems. Very, very pretty and make a great cut flower, but what are they???