The light and strong category doesn't exist. Unless you go custom :'(
Remember custom doesn't necessarily mean good :'(
Now for the part of my post which isn't smartass...
For going light there is only one method that really works: Don't bring it with you. What I like to focus on is the heaviest items because they have the greatest opportunity for weight loss. Earlier this year I did the exercise of weighing everything I take day touring down to the skin and I found that I was at a shocking ~42 pounds. I was even more shocked to find that there really weren't many places to cut weight and still have a reasonable margin of safety in terms of what I was carrying. I can proudly say I am now at 31 by getting lighter skis and boots then dumping the things I don't really use and/or aren't multipurpose. I didn't really replace that many items, just looked very very closely at what I was carrying. When it turns from day trip to overnight or multi-day, I focus even more on eliminating items which aren't multipurpose. I can definitely support the cilogear idea, especially if you use the back padding as part of your sleeping system.
Of the items you mentioned, the ones which I see as the biggest opportunities were the backpack, sleeping pad, and maybe crampons. Hard to say without know what you are using, but generally speaking it is going to be hard to get a good weight to dollar ratio improvement on a shovel, probe, or ice ax.
Then there is the time based economics to look at. As in I would rather lose 1 pound on something I take every single day than 2 pounds on something I take only a few times a year.
I saw the best combination of [weight loss/ price / frequency used] by putting money into my ski/binding/boot system.
