The keys F2-F4 in byobu are disfunction in Gentoo. In https://answers.launchpad.net/byobu/+question/118308 I found the reason and a fix. Appearently the section XTERM TWEAKS in /etc/screenrc does something to these keys via termcapinfo xterm 'k1=\E[11~:k2=\E[12~:k3=\E[13~:k4=\E[14~' Replacing that with termcapinfo xterm 'k1=\EOP:k2=\EOQ:k3=\EOR:k4=\EOS' fixed it.
It might also work properly if you simply deleted the line.
in /etc/screenrc , commenting out # termcapinfo xterm* 'k1=\E[11~:k2=\E[12~:k3=\E[13~:k4=\E[14~' seems to have fixed it -- word of warning is that this is strictly a console-only install as of now and I don't have xterm