Why did oiling cause this crank to become dirty?
The oil that you applied to the crank joints is doing several things. 


Foremost it has eliminated the dryness in the joints that led to the squeaking.
It is flushing out the years worth of wear dust and particulate that collected in the joints from operating them without lubrication.
Oil present on the joints now will be a magnet for new dust and dirt from the area nearby the crank rod, although this is a relatively minor issue.


The primary factor that is leading to the 'dirtyness' is the second point above. So you may want to look into thoroughly cleaning joints with something that can penetrate into the wear areas and flush out all the old crud. This could be achieved by either removing the crank and moving it to a convenient work are or done in place. If you remove the crank you may get effective results by soaking and working the moving parts in a bath of warm soapy water. If done in place you may have luck with using a penetrating type cleaner that comes in a spray can with a nozzle tube. (Note that if you spray in place hold the rod and joint in an old cloth or rag so the spray does not get all over everything else nearby).

Once the joints are nice and clean you have any number of options for lubricating the joints for smooth operation. Using the oil again is an option but it would take a very small amount. A dry lubricant such as a silicon spray may work well if applied right down into the joints with a nozzle tube. The key to the lubrication is to eliminate or significantly reduce the wear on the moving parts.