How do I get the best possible texture when making vegetable cream soups? Many recipes call for straining the almost finished soup to get rid of any extra chunky bits and get the best mouthfeel. But I am really confused, because with any reasonably fine sieve I filter out almost all of the vegetable matter and end up with a very thin soup.

Not mentioning it's hard to actually finish the filtering process, because the sieve gets all cluttered. The same goes for certain sauces such as Bechamel. Not sure how I can strain the sauce, because it's so thick and doesn't go through the sieve very easily.

What's the best way to achieve really smooth soups and sauces? What kind of sieve should be used?
You could always blend before you strain.  I find that when making soup of all kinds that a few minutes with my immersion blender does wonders for the final product.  Not only does it puree all the solids into much smaller chunks, but it also makes sure that all the liquid is a homogeneous whole.  

After blending, I also tend to strain just to get out anything that I might have missed.  I use a fine mesh strainer and a spatula to force the liquid through quickly.  I also own an old flour sifter that I have used quite a few times instead of the strainer, but it doesn't offer any real benefits over the other.