Is there a lubricant that can be used for linear bearings, bronze sinter bushings and threaded rods alike?
A mid-weight PTFE grease like the popular Superlube will work in all the cases you mention (bearings, screws, and sintered bushings). 3D printer service conditions are quite light-duty as far as lubricants are concerned. You really just need to keep everything a little bit "wet" with oil or grease and performance will be adequate. 

The main downside to using grease with sintered bushings is that they will likely stop being "self-lubricating" after the first exposure. The grease tends to clog the pores that allow the sintered bushings' factory oil impregnation to maintain a nice oil film on the sliding surfaces. So the bushings will forever-after require regular re-greasing, just like the ball bearings and threaded rod. 

In comparison, a light machine oil like 3-in-one will maintain the sintered bushings' self-lubricating properties, but if used in ball bearings and screws will require very frequent replenishment. And that is certainly an option -- oil DOES work on bearings and screws -- but odds are good that you'll eventually over-oil the bearings, get drips on the build plate, and bang your head against a wall trying to figure out why your prints won't stick all of a sudden. Grease doesn't need to be applied as often, and it tends to stay where you put it rather than dripping. So grease is generally preferred to oil if you have to pick just one lubricant.

Again, the most important thing is to keep sliding and rolling surfaces wet with something. You'll just have various maintenance trade-offs with different options.