The piece is a radius and angle dresser tool for shaping grinding wheels. The shaped grinding wheel is then used for grinding tool bits or special shapes. It has a diamond bit at the end of the tool bar.
Humidity is a problem in this area too. The problem could be the oil you're using. You didn't say what you're using but WD-40 is worthless in this case. Use way oil on the slide surfaces. LPS#3 is a good long term coating for other parts. It's a little waxy but for long stretches between use, it's probably the best. Keep things coated even if you have to make it a weekly job. Reducing the humidity and/or controlling temperature swings are the best way. Not knowing your situation makes it hard to define a solution. A 60w light bulb tucked into a machine can help too.