I'm at a lost, but let's try to diagnose and narrow down the problem. Something might pop up along the way.
First, you mentioned that
date | tee -a logfile
works, so the problem is not likely to be either tee or bash's pipes. Maybe you can try other programs and see if they work as well. Anyway so far the problem seems to be with echo.
#echo something | wc
1 1 10
seems to imply that echo is indeed printing to stdout.
Maybe you can try
to see if any alias for echo have been defined.
Also check that you get the following results (which I think you'll get based on the wc test)
#echo something > filea
#echo something 2> fileb
Does echo something | tee -a logfile work as a normal user but not as root?
BTW, I'm not implying that you run the commands as root by using # as the shell prompt. Run them as whichever acct that gives you the problem.
got to go for tutorial. will check back with you if I think of anything else.