It's always 5 o'clock somewhere
After a long day of absurdist bits, sophisticated grifts, failed paradox resolution attempts and their usual drunken shenanigans, the Odd Little Men like to clock out and dip over to the Tavern for a pint.
It is a humble, unassuming establishment with a circular wooden door. A weathered sign reads "Tavern" and sways gently on thin brass chains when the door is open or shut. Inside, it looks more or less like any bar: tables for seating, a bar (staffed by Odd Little Men) with various bottles of exotic and common liquors. On one wall is a long row of tapped kegs that seem to be cycled in and out with regularity as they are emptied, and steps that lead to an extra seating area for overflow.
A maître d' guards the entrance. He has a list. It's long, considering their number (infinite), if you're not on the list you'll be waiting a long time while he checks in vain for your name. Most visitors eventually get the hint and give up.
But you didn't leave. You slipped in while the maître d' was distracted by a heated argument between two Odd Little Men over whether a particular keg counted as "empty" when it still produced foam. You ducked under a table, crawled past a curtain, and now you're in.