My understanding is that barley straw releases something that will inhibit algal growth, thus in time clearing water
of algae.
http://www.naturalsolutionsetc.com/BarleyAbout.htm
http://ohioline.osu.edu/a-fact/0012.html
I'll also assume your problem is suspended clay in water (silt and sand settle quickly). Clay stays suspended in water because it has ionic charges distributed on the outside of the minute clay particles, with the opposite charge hidden inside the particle. Water molecules are polar - positive and negative charges on opposite ends - and they can pick up the clay particles and keep them suspended.
To settle suspended clay from water, you need to change the ionic (electrical) environment in the water. To do this, you can introduce highly-charged ions. This implies heavy elements. Many heavy metals are poisonous, but one of the easiest safe sources of heavy ions is cement, which for this purpose provides calcium. Get two bowls or better still large clear glass jars of the muddy water, add a small pinch of cement powder (pure - not premixed with sand) TO ONE ONLY (keep the other for comparision), stir and then leave overnight. In the morning you'll find at least some of the suspended clay has flocculated (think of it as flocking together around the highly-charged heavy ions) into soft goop, and settled.
OK, take your cement to the pond. If you have a boat use it, otherwise get on the upwind side of the pond. Mix a little (cupful of) cement powder into a bucket of water, and throw it, spreading widely, into the pond. If you have a pump that can handle this without being damaged by the suspended cement powder, use it. Repeat, moving around the pond. You should place more of your effort from the upwind side, as you can throw the water further from there and the wind will also help spread it. You might also stir the water with a shovel after you throw each bucket in.
Don't overdo it. Come back every second day for a week and repeat. Oh, yes - take photos that show the colour of the water before you start each time, and at the end.
This won't clear it altogether, but it will sure help.