After a few rounds of drinks, everyone was chatting with a buzz on.
Tips
usage
醉意 describes the visible or felt signs of being a bit drunk, not full drunkenness (that's 醉 or 喝醉了). Common collocations: 几分醉意 (a touch tipsy), 带着醉意 (with a buzz), 睡意 (sleepiness) is the parallel formation for sleep.