Things have changed, haven't they? When I set up my planted tank in the 1990's I had to glean tidbits from FAMA and TFH and there sure wasn't much. Library and bookstores had zip, my old 1960's Axelrod 3 ring binder thing was better than most of what was there.
Feed the plants! With a bright CO2 enriched tank the fish poop is unlikely to provide enough of the essentials to grow strong plants that won't allow algae to land and grow. See the crypt leaf? It is on its way out and that is why the algae could grow. Trim any damaged leaves you see, they will just serve as places for algae to grow. Look at the Fertilizer and Water forum's sticky thread to see how to and get a set of dry fertilizers so your plants have all they need to grow. Excess nutrients don't cause algae, they help the plants to grow strong and healthy! I have no green spot algae because I dose a lot of phosphate [understand that is in combination with all the CO2 the tank gets as well] and ended a horrible siege of green water by dosing nitrate. Alas that never helped again but low nitrate was the reason I had that particular case of green water.
Do cut the hairgrass back to the substrate best you can. It does brilliantly trimmed, better than a lawn as the tips don't even turn brown! While it is short go ahead and vacuum the area as hairgrass traps debris and sometimes that encourages algae.
If the microsword hasn't been in the tank long I would pull it out, sit down and pick out all the wiry stuff then replant the clean microsword. This will be very nitpicky and annoying and you will likely end up with individual plantlets that need to be replanted using tweezers. I have had tiny colonies of clado rarely so I don't remember if it attaches firmly or not. If you are lucky it isn't attached just winds around the plants. Next best would be if it does attach but each algal plant winds around and is only attached in a few spots.
Last time I had staghorn I zapped it with Excel and moved the powerhead to blow across the area. It turned pink and then the otos and platies ate it all up. Might consider investing in a bottle of the stuff. You dose it by turning off the pumps so the water is still and use a syringe to squirt on problem areas. I use about 1.5 ml per 10 gallons. Let the tank sit for about 20 minutes then turn on the pumps. The red algae like staghorn and BBA will turn red and then the fish can eat it. Otherwise it dissolves over a long period of time. That stuff is tough and takes a long time to decay. I don't know if it kills clado or green thread as I haven't ever had a problem with them. Pick out as much as you can before dosing though, no point in killing algae on dying leaves!
In summary. Find out about fertilizing and get a set of powders. Remove damaged material including mowing the hairgrass. Clean the substrate of debris and be sure your filter is in good order. Pull out as much as you can off plants you need to save. Consider using Seachem Excel to zap spots you cannot remove.