I believe the 'alphabetical' order you're actually looking for is:
alien, beetle, seaman, dealer, eastern, effort, jeans, island, jailbird, canine, elevate, eminent, enter, open, peachy, cucumber, arson, estimate, teenager, eunuch, veto, expert, wiring, zebra
Since:
The first syllable (or thereabouts) of these words sounds like a letter of the English alphabet:
Alien, BEEtle, SEAman, DEAler, EAstern, EFFort, JEAns, Island, JAIlbird, CAnine, ELevate, EMinent, ENter, Open, PEAchy, CUcumber, ARson, EStimate, TEEnager, EUnuch, VEto, EXpert, WIring, ZEbra
Here, all letters of the English alphabet with the exception of 'H' and 'W' are represented. Good luck finding a dictionary which will list them in this way! ;-)