There are three variables for a bowlers stats: Wickets taken, Runs conceded, balls bowled.
Each of the three main stats is a ratio of two of these variables. Each ratio helps tells its own story and looked at in combination, tell the overall story.
Average - runs/wickets - tells the story of the bowlers effectivness at limiting the oppositions overall score.
Strike Rate - balls/wickets - tells the story of the likelyhood of a bowler taking a wicket.
Economy rate - runs/(balls/6) - tells the story of the likelyhood of a bowler being carted all over the park or not.
For an individual bowler therefore, the average is the best indicator of effectiveness, as limiting an opposition's total is the ONLY objective in the feilding faze of the game.
A bowler with a so-so average and poor economy rate can be very effective if the have a good strike rate, however this relies on the quality of the other bowlers around him who need to have low economy rates and or averages to limit the scoring while Mr so-so Average gets wickets and gets carted.
Therefore Average tells the best story of a bowlers total worth, while strike-rate tells more about how useful a bowler is in a total bowling attack.

cheers
(Gee I hope that drivel makes sense)