Of course, localectl is missing, it's a part of systemd. But your problem can be solved without systemd, it's simple. There are two different parts: localization of tty (console) and localization of X11.
Localization of console in Artix is done by creating and editing /etc/vconsole.conf. You should add KEYMAP definition there. For example, here is my /etc/vconsole.conf:
LOCALE="en_US.UTF-8"
KEYMAP="ruwin_alt_sh-UTF-8"
FONT="ter-v16b"
CONSOLEMAP=""
This allows me to switch between English and Russian keymaps by pressing Alt+Shift. Keymaps are stored in the /usr/share/kbd/keymaps/i386/qwerty directory. There is a couple of Greek keymaps: gr and gr-pc. Those are compressed text files, just look inside and read the commentary to learn how to switch between languages in each keymap, and then choose whichever you like.
Then, localization of X11. As already mentioned before, this can be done by executing setxkbmap. But this can be done automatically by Xorg during the startup. Just add the file /etc/X11/xorg.conf.d/10-keyboard.conf with something like that:
Section "InputClass"
Identifier "MyPreciousKeyboard"
MatchIsKeyboard "on"
Option "XkbLayout" "us,ru"
Option "XkbVariant" ","
Option "XkbOptions" "grp:alt_shift_toggle,terminate:ctrl_alt_bksp,grp_led:scroll,numpad:microsoft"
EndSection
These are options transferred to setxkbmap. switching by Alt+Shift, Ctrl+Alt+Backspace terminates X11 session, scroll lock keyboard indicator shows the current layout, numpad keys work as in Windows (you can use Alt/Ctrl/Shift + arrows/home/end/etc).
Option XkbVariant sets the variant of keymaps: for the first keymap before the comma, and for the second one after the comma. In my case, there are no specific variants, thus the "basic" variant is used. You can learn what variants your preferred keymap has by inspecting the /usr/share/X11/xkb/symbols directory. Just look inside the desired file, in your case it's gr. Variants are defined by strings like xkb_symbols "blah-blah-blah". For the Greek, there is a particular variant polytonic, which allows you to type Ancient Greek diacritics. Ὑγιαίνῃ!