This is the 10324th most frequent Japanese word.
飲も
"飲も" (nomo) is a casual imperative form meaning "Let's drink."
飲もう is used in the volitional form, expressing a suggestion or intention for drinking.
お茶を飲もう。
Let's drink tea.
飲み放題 uses 飲む as the base of a compound noun, relating to drinking without limits.
今日は飲み放題だ！
Today is all-you-can-drink!
飲んだ is the past tense of 飲む, indicating the action of drinking in the past.