Energy-optimal beer cooling

There is probably a slight energy advantage to putting the beer in the fridge.

As explained by Joe Iddon, it will take a fixed amount of energy to cool your beers, and it always takes a certain amount of power to maintain the temperature of your fridge when it is on and closed. Considering only those two factors, it makes no difference when you put the beers in your fridge.

However, because you say that your fridge is in use in the intervening time, you should also consider how the fridge behaves when you open it. When you open the door, it trades some air with the outside. When you close the door, it cools down the "new" air. If you put the beers in the fridge, there is less air in it and consequently less new air after opening and closing the door. (It may be more important that the beer blocks air currents, but the effect is the same.) So your beer actually makes the fridge slightly more resilient when the door is opened and closed.

For completeness, though, if you open the door long enough to significantly warm up the beer, then you could do yourself some harm because the beer will take more energy to cool down than the same volume of room temperature air, but I estimate that you would have to leave the door open a lot for that to happen: As long as the air heating up the beer stays in the fridge, it is that much less heat energy that the fridge needs to pump back out when the door is closed.

To get the beers from room temperature to "cold" temperature will require a fixed amount of energy to be transferred from the beers, given by $q=mC\Delta T$.

Once you have cooled the beer, and the beer is in an environment (the fridge) that is the same temperature, the beer will not get any hotter, hence it will not need to be cooled down again, so therefore, no matter how long you leave it, no more energy will need to be transferred to the beers. So we should conclude that the two scenarios require your fridge to consume the same amount of energy.

However, this does not account for the interface between the fridge environment and the room environment. Namely, the room is trying to warm up the fridge, even with no beers in it. This means that the fridge must be consuming an amount of energy per second, $\frac{dq}{dt}$, just to counteract the heat flow from the environment, $h = \frac{dT}{dt}$.

Therefore, for optimal beer cooling, you should keep your fridge off until the last minute, before putting the beers in just in time for them to cool. This way it does not waste energy fighting the environment whilst the beer is already at temperature.

However, by virtue of your fridge being "half-empty", I doubt switching it off is an option.

Therefore we return to our original answer: they are both the same.

Once the beer is cold, it will not matter how long you keep it cold, as the fridge keeps a constant temp. The beer would have to get warm again to require more cooling. However cooling your beer now might result in running out of beer by the time of the party.