is there any LEGAL way (w/o jailbreak) to install iOS application to iOS device (ipad, iphone, ipod) without publishing to application store? For example - application for closed group of users (admins/moderators etc of some web application).
Apple supports "Ad-Hoc" application distribution for exactly this purpose, but it is limited to 100 devices. If you have an Enterprise developer account, you can do Ad-hoc distribution within your organization, as well.
iOS Developer Distribution Options
iOS Developer Enterprise Program