I want to install some more software on sabayon live and they should be remained in USB for later use. Can I install packages on live Linux OS?
Yes you can, typically, but these will be lost when you do a reboot if the medium is read only, such as a CD and/or DVD. I've done this from time to time when needing to recover passwords from NTLM systems and not having an actual LiveCD handy that includes the recovery software.
So in a pinch I've booted using an Ubuntu LiveCD and then installed the necessary software, and recovered the NTLM passwords from a Windows partition.
With a USB flash drive that includes a live installation you're likely going to find that you still cannot install software either. Sometimes there is a reserved area where you can park addon applications which will then get pulled into the Live system upon bootup, but it's generally recommended that you install the Live distro instead on the removable media if you intend to customize it in any fashion.
I realize you're working with Sabayon, but I did find this AskUbuntu Q&A titled: How to customize the Ubuntu Live CD? which shows a farily detailed and painful looking process one would need to go through if you wanted to customize the packages of an actual Live distro. Similar steps would likely be required for Sabayon as well.