A new player spawned on the server for the first time and was spawned inside a tree within the protected area around the spawn. We don't have an admin around, but he is obviously stuck since he can't destroy any block around him and has no way out without destroying something. What can he/we do?
Although this is a more long-term solution, since your admin is not around presently as you mentioned, you should consider getting them to add some mods that allow for Admin-style commands. Plenty of good frameworks already exist that have everything you need - Essentials is a pretty decent choice. Using such systems, the ability to manually move a player from one location to another is just a simple matter of using a "teleport" command or such.
If the server is on Hard mode, just walk away. Over time, the player's hunger bar will deplete, causing his life to deplete, until he dies. Since spawning is slightly random, you'll respawn most likely in a different position.
On normal or below, you'll have to get more creative about killing him. If another player can reach him, a simple wooden sword could dispatch him (particularly after starving). If an op can be located, the "/kill" command would work, but I notice you said above that you lack permissions to "/kill" in this situation.
Have him log out, then fill the space he was standing in, and then have him log back in. Since he can't be placed inside the now-occupied area, he should respawn above it. Repeat this process if necessary until he spawns in a useful location.
As far as I can remember, you can usually place objects in the spawn location, although you can't remove them once they're there.