I read somewhere that the On Screen Display overlay can be used to display things like caller ID from your land line phone when it rings. Does anyone have this working on LinHes?

From what I can tell from Googling, you would need something called ncid (Network Caller ID) server and client installed, plus a modem and modem drivers installed. Neither of which seem to be in the LinHes repositories as far as I can tell.

A lot of modems are "winModems" and it looks like maybe the kernel needs to be recompiled to support them? I'm quite the Linux noob, so a lot of what I read goes right over my head.

Nope, those programs aren't in the repo. Some "winmodems" will work with Linux via "linmodem". Support for those aren't included in the distro either.