That unsightly green fungus growing on your oak tree's bark is actually lichen, which is a combination of fungi plus algae. The lichen's presence indicates that your environment is free from pollutants. Lichen won't harm your oak tree, but it does indicate weak foliage cover, since sun promotes lichen growth. While you may be pleased to know you have good air quality, if you find lichens on your oak tree unsightly you have a few options.
Scrub the lichen with a stiff-bristled wire brush to dislodge it from your oak tree's limbs. This may work on some lichens, especially if they are new. You won't be scrubbing powerfully enough to harm your oak tree.
Wet the lichen with water, then repeat the scrubbing one more time.
Cut off affected branches with anvil pruners if the damage is on limbs, not on the trunk. This will spur new growth on your oak tree, which will up your foliage cover. Pruning also increases air circulation, which cuts down on the likelihood of fungus or bacteria sticking around your oak tree.
Treat your oak tree with a copper-based fungicide that is approved for use in your area, as horticulturists from Texas A & M suggest. Check with your local county extension office for a list of approved fungicides.