My kitchen items end up getting a sticky grease coating when I cook regularly. Things not even near the stove top. I don't have an overhead fan, what can I do about this? 
A cooker/range hood. The proper sort will suck in all that greasy fumes, pass them through a carbon filter (which needs changing) and vents it outside, or upwards(in smaller kitchens without a place to vent it. Its also helpful if you're cooking something that may have irritating fumes.   There's pretty much nothing that will mitigate the problem as well.  