Use a mixture of 1 part bleach with 3 parts water (like 1 quart bleach mixed with 3 quarts of water.) Use a light, bristle brush to do the scrubbing. Start from the bottom and work your way up. If you start from the top, you'll end up creating 'clean streaks' on the siding as it washes down on the dirty siding. Wet the walls a little at a time, then go to it. Use a large bucket or pan and a soft-bristle broom, if necessary. Cover your trees and schrubs and plants BEFORE you apply the cleaning solution. Bleach will do damage! If you want to wait until early Fall, that may be better.
In the mean time, you might want to take some measures to reduce or even eliminate your 'problem'. But before you do, you need to know what causes mold and mildew and algea to grow. These 'bad guys' like damp, warm conditions, where there's little air flow. So, if you alter ANY or all of these 'conditions', you'll dramatically reduce your problem. Here are some tips.
Plants and trees should be kept at least 2' from the house. This way, air can travel 'along' the perimeter of the entire house unobstructed. Make sure your gutters and downspouts are working properly. In the next rainstorm, put on your raincoat and boots and grab an umbrella (as long as lightening is absent) and take a walk around your house. Make sure your gutters aren't overflowing. They should be draining into the downspouts. If they're overflowing or leaking, repairs need to be made. Also, make sure your downspouts don't dump water within 3' of the foundation. You should have a slope of at least a couple of inches AWAY from the foundation, for that distance of 3'. This way, water doesn't pool at the base of the house. (Termites and water bugs LOVE these conditions too!) If your trees are over-grown, prune them back. Let the sun in! Prune any bushes around the house too. If you want to move them to that 2' distance, do so. Or, remove them and plant new ones.
IN closing, if you can dry out the ground, improve air flow, and let the sun in, you'll dramatically improve your current situation! My best to ya and hope this helps.
PS: Whenever planting bushes or flowers, remember, when they're FULL-GROWN, no part of the foliage should be withing that 2' 'distance' from the foundation. Soooo, if you have a bush that you want to grow to a RADIUS (not DIAMETER) of 3', plant it 5' from the house. (That's 2', for distance from the house, PLUS the 3' radius EQUALS 5'. Radius = 1/2 Diameter ...) Always do your calculation on what you want the plant to be at full-growth. The location you plant it may seem like it's REALLY far away from the house, but when it's full-grown, you'll see that it's within 2' of the house! Plus, this 2' buffer zone allows you to do things like 'clean' the house, do weeding, and pruning.