Menu Bar On The Right/Left Side?

I have so many modules and I want to display them on top, and on the left/right side or both sides. It's because most of the visitors don't spend time looking for hidden stuff unless they SEE them. 

The NYPOST.com  change their system to CMS which displaying pictures along with the stories has increased 40% in traffic and 50% increase in clickthrough rate.

I don't know if you can split the menu into two; and I am not so sure about a left menu and a right menu.  You can split the top menu into rows, there is a module in the market for this.  For other menu changes, look in the market at the different menu modules available.  If you have questions about a module, click on the message button and talk with the vendor first before buying.

what I want is the additional menu(s) bar on the side. I don't want to crowd the header so spread the modules around the sides. 

You will have to create one yourself by hand. There are no modules in the market that will allow you to move main menu items to a menu you can pin to the left or right side.

I see this one is cool

http://www.demozzz.ru/d71/index.php?skin=gpl

The menu is on the left side, but instead of the big search box on top, we will replace it with an additional menu bar would be perfect. Total will have at least 20 modules displaying right in the face of the visitors.

I believe that is a theme(skin). Not a separate menu.

Yes, that is a theme; it will change the entire look of your website.  You can try contact AndrewP and see if he can design a menu replacement similar to what you want from the theme.  Andrew actually has some menu modules.  Look under Navigation in the Market categories to see what menu replacements are available.