It's possible there are two are things going on, but we're getting into the area where I'm not the expert.

1) The green. You MAY have a high metal content in the water. Take a sample to a pool store and ask them to test for metals. Do NOT let them talk you into adding more calcium (they'll absolutely INSIST with a CH of 70 you need it. You don't--your pool is vinyl and it's only for concrete/tile/plaster pools). If metals are high, there is a metal dissolver, a sequestrant to use. HEDP is the best stuff, like Jack's Magic (Pink). Then you'll need to let FC come 'way down before you use it. If it's metals, the high FC can cause the water to be green. HEDP dissolves the metal so it stays in suspension, but only water replacement actually gets it out--but the HEDP lets you live with it. Again, I'm not the expert on metals in water.

2) The cloudiness. If you do, indeed, have a high metal content, then you probably have something suspended that's too fine for the filter and even the skimmer socks. There are two things that then may help. You can try either a flocculant or clarifier, but not both. Personally, I like using PolyQuat. It's not only the best algaecide (besides chlorine), it also can act to clear water of suspended particles too small for filtering. There's also a gadget called a "Slime Bag" that goes over the return. They are a bit pricier, in the $50 range, but filter far finer than skimmer socks and people seem to have good luck with them.

There's one other possibility and that is that something else is going on that requires one of our chemistry experts, either Chem_Geek or PoolDoc himself, who's been out of touch since November. Again, we are out of my area a bit now as I'm neither the metals expert nor the special situations expert.