How can I deal with the "floppiness" of tall rockets?

Don't do this! It's bad, bad, bad!

Even by adding struts as per @char1es' answer, your rocket still isn't structurally sound. The reason for this, as I've said before in other answers, is that the topology of a KSP rocket is in the form of a tree. This means that only one of the stack decouplers is attached to the bottom quad coupler. The result is that the other three are left "floating", and have no problem clipping through the other parts of the rocket.

No, what you want to be doing is using a single rocket with similar thrust and specific impulse to the combined 4 rockets. For the second stage, I'd hazard a guess that the skipper is probably what you want, while for the upper stage you probably want an LV-909.

As an aside, if your rocket can't support its own weight on the launch pad, it's not going to survive launch. If there's significant flex without it even moving, you may have done something evil, and at the very least something immoral. There are usually better approaches than doing stuff that's evil and/or immoral.

This may not be the most aesthetically pleasing solution but this is what i find works best for tall "wobbly" rockets.

You need to build an external frame around the rocket using struts and i-beams.

1. add horizontal i-beams at the center of your craft in radial pattern.
2. next add struts from a lower part of the craft
3. add struts from the i-beams to the "wobbly" part of your craft (top)

You can add as many levels of i-beams as you want, but keep in mind that it takes a certain amount of force to break the struts supporting your craft.

edit: this will not work for the quad-decoupler in the middle of the rocket, as mentioned by @MBraedley. However it works quite well for most excessively tall rockets.

This answer is for the more general case, however in your case, you cannot improve structural integrity because of the tree topology, as mentioned by @MBraedley.

      /\
     /__\
     |  |
    /|  |\
   / |  | \  <== Struts
  / /____\ \
 /  |    |  \
====|    |====  <== I-Beams
 \  |    |  /
  \ |    | /  <== Struts
   \|    |/
    |    |
    |____|
    ||||||