Some are logging data and some are error log. Anyway, I found the resolution to make it and become quiet in my CLI console now.
In non-daemon mode IAXmodem does not detach itself from the controlling
tty, and it does send logging data both to standard output (informational
items) and to standard error (errors). As this logging can be a bit
verbose, you may choose to ignore all of it by starting IAXmodem like
this:
/path/to/iaxmodem ttyIAX >/dev/null 2>&1
; the addition of latter part in the statement works.