Answer:
It doesn't live within a house, nor does it live without. Most will use it when they come in, and again when they go out.
Gets rid of bad ones, short and tall. Tightens when used, one size fits all.
I am seen in the water. If seen in the sky, I am in the rainbow, a jay's feather, and lapis lazuli.
Always old, sometimes new. Never sad, sometimes blue. Never empty, sometimes full. Never pushes, always pulls.
A mighty weapon in the war against winged household pests.
People take me on walks and I run and have fun. What am I?