Thank you for your question about the moss and lichen on your tree's stems.  Actually, they are not harmful to the tree unless they retain so much water, either rain or ice, that their weight may become an issue.  A moss is a plant; a lichen is a symbiotic combination of an alga and a fungus.  Having lichen in your neighborhood means you have clean air, since they don't grow in polluted environments.  The moss help to remove contaminants from the air as well, by trapping them.  So, be thankful they're growing in your trees.  They neither hurt nor help them.   But if you really feel they need to be controlled, this Extension article gives more information about them and the control issue.  Good luck!

Thanks, it's always good to find out that the weird looking stuff are truly beneficial.

It is!  In fact, if you drive south on I-5, you won't find lichen west of the highway near Wah Chang in Albany, due to persistent fallout of radioactive chemicals.  And moss was recently utilized to identify harmful chemicals emitted from at least one Portland factory.  In fact, planting moss is considered to be one way to manage pollution!  Perhaps your neighbors and you should have a moss celebration!