Yes, I suggest a total cleaning of the tank. That means removing the fish and then soaking everything that's not alive in dilute bleach. I bleach soak tanks and aquarium ornaments a lot. I would also save the biological filter (pull it out and store in aquarium water) and not bleach that. It may bring algae back into the new tank but without it, the ammonia and nitrite will spike.
Once the tank is set back up, I suggest weekly 30-40% water changes with gravel vacuuming. I add Stress-Coat (dechlorinator but I use it to detoxify copper from the pipes; I don't have chlorine since I have well water), Stress-Zyme (good bacteria), and aquarium salt (a tablespoon per 5 gallons of new water) with water changes.
To control algae in aquariums, check out
http://www.fishpondinfo.com/plants/algae.htmThis is from my web site about tearing down tanks:
"Occasionally, you may decide to tear down a tank. This means removing everything, cleaning everything, and setting everything back up. Reasons to consider such a drastic step include: uncontrollable pest or disease outbreak, large change in water quality to dangerous levels, large amount of fish deaths, a tank too beyond dirty to clean without tearing it apart, a total crash (that means everything dies), a lot of live plants dying, lots of algae, simply creating or getting rid of a setup, etc. I have torn down tanks when I have gotten new tanks and moved a lot of fish around, due to uncontrollable planaria outbreaks, a few times when most of my fish died, and also when the tank gets super dirty.
The first step is to provide a temporary home for any plants or animals. A small tank or bucket works. Fill it with water from the main tank (unless you are tearing down due to water quality in which case well-aerated, fresh water with additives at a similar temperature is better) and aerate it well. Move the fish and any other living things. Separate the little and big fish so they do not harass each other. Next, drain most of the tank water. Then, remove all the ornaments, rocks, gravel, etc. Soak these in a 1:20 bleach solution for a few hours. After that, soak them in fresh water with dechlorinator for a few hours. In the mean time, wash the tank out. After getting all visible dirt, algae, etc. off, rinse with the dilute bleach. Then rinse with fresh water with dechlorinator. Rinse and rinse a lot. If there are no fish to worry about, you can fill the tank back up and add some bleach to let it soak for an entire day. Then, drain and refill with fresh water and dechlorinator. Let that soak another day and then drain again.
Set the tank back up. Rinse the gravel in a bucket again and put back in the tank using water to help. Fill the tank half full with tap water. Put in any ornaments, etc. You can also wash the live plants in the same bleach solution and then dechlorinator but for only about 10 minutes in each. Remove dead parts, rub off algae, re-clump certain plants together, and put the plants back. Fill the tank to the top and add any additives (dechlorinator, live bacteria, and a little aquarium salt are important choices). See here for information on water additives. Add aeration and full filtration. If any live animals can stay in their temporary quarters overnight, that is best. Aerate the water overnight before adding animals back. Watch them for distress. Now, you have essentially a new tank."
Good luck!