I've never strained my juices.  I've used an old Juiceman II and while the pulp has been a tad bit juicy lately, I've never had pulp in the juice itself.  Unless you have a serious amount of pulp in your juice I would not strain it and if you do have a serious amount of pulp in your juices, I would look into a more convenient and cost effective juicer than the one you're using.

Another thing, it is in my humble opinion that one needs to be drinking these fresh raw juices asap.  The more the juices are exposed to the air the quicker the juices oxidate and die.  Much like watching a potato, apple or banana turn brown when exposed to the air. The enzymes die off. Something to take into consideration.

Try to make your greens as dark green as possible.  Such as spinach, bell peppers, brocolli, dark green leaves have more chlorophyll than the lighter colored leaves found in some of the lettuces.

There are many types of juice recipes found on my blog: http://curezone.com/blogs/m.asp?f=573&i=78

My usual is 4 or 5 large carrots, a couple apples, and then handfuls of spinach, dandelion greens, brocolli, kale, celery, whatever's dark green, lately I've added wheatgrass... I do 16 ounces per glass, with half of that (8 ounces) greens... the rest is carrot/apple.  Tastes pretty good and is so powerful!  The carrots and apples mask the tastes of the greens.

I wish you the best in your journey... juicing can change lives.

~ Dazzle