Thank you for your tips. I was doing everything correctly (maybe). Because I found compiled lan78xx.ko. Previously I was looking in the wrong folder. And my second mistake was that after flashing image into Omega I expected that module will be list when I type lsmod but it lists only installed modules but not the statically built-in kernel. Does someone know how to list kernel built-in modules?
Tip for somebody who needs a driver that source is part of the kernel already.
make kernel_menuconfig find there your driver and mark it * for the static part of the kernel or M for a module.
make world
or only recompile kernel - it is much faster.
make target/linux/compile you will find compiled .ko if you want to install it with insmod
or you can continue with
make target/linux/install and
make target/install and you will get new .bin image with recompiled kernel