The Turris Omnia Router runs OpenWRT so there are Zabbix Packages available to monitor it.
Simply type following command in the turris shell:
opkg install zabbix-agentd zabbix-extra-network zabbix-extra-wifi zabbix-get zabbix-sender
and edit your config file /etc/zabbix_agentd.conf
Server=your.zabbix-server-ip.address.here
save, and restart with
/etc/init.d/zabbix-agent restart