"How can I tell quantitively [at home] whether a lens is sharp or not ?"
Print up 5 sheets of the same line of type double spaced from 8 point to 72 point, with the type size included at the end of each line. This should fill the page. Set up your camera with a 50mm lens 10 feet from the wall. Make sure the camera is level and square to the wall. Tape one sheet on the wall so that it is in the center of your viewfinder. Tape the other four sheets so that they are in the corners. Lock up your mirror and use a cable release. Shoot at all apertures. Look at the RAW files at 100%. I consider a lens sharp when you can read the 12 point line in the center and corners--as I can with my Carl Zeiss 50mm 1.7 on my Canon 1DsMkII. This test will also tell you the best apertures to shoot at. You will notice that most lenses go soft at f16 and 22. Some of my lenses are sharpest at 5.6, others 8, some at 11.
Then test each lens in your kit so that the four corner sheets fill your frame. In this way, you can compare the resolution of your primes and zooms at various focal lengths.
You can also check the contrast of your lens. Is the black of the 72 point type really black, or is it blue or brown? Are the edges of the number sharp, or are they fuzzy? The 72 should be black with sharp edges.
To check focus accuracy, tape a yardstick to a wall, set up your camera at 45 degrees to the wall and focus on a number on the yardstick with the lens wide open. Look at the RAW file at 100%. I don't worry if the lens is half an inch off as I don't shoot wide open. If you do, you will want to get it corrected.
Finally, you will want to check focus at infinity. I do this by shooting a commercial sign at a distance of 100 feet or more with the lens wide open, and then examine the RAW files at 100%.
Don't use JPEG on your tests. It really degrades resolution.