I don't think what you want is possible. See this superuser thread titled: How do I detach a process from Terminal, entirely?.
I think you have essentially 3 options.
Option #1
Run the scripts that are polluting you terminal such that they're run like so:
nohup somescript &> /dev/null &
Which should run their STDOUT & STDIN to /dev/null, background them, and disconnect them from your terminal's signals if you should close it.
Option #2
Use something like screen. Thanks to @StephaneChazelas in the comments it does appear that there are screen packages available for Debian on your architecture.
Option #3
If you don't care if you temporarily pause the processes that are polluting your terminal's STDOUT you can use this setting: stty tostop. This has the effect of stopping these processes from sending their STDOUT to your terminal. When you're done you can re-enable it with the command stty -nostop. I found this in the Unix Power Tools 3rd edition book.
example
Here's my example app that is polluting my terminal's STDOUT:
$ while [ 1 ];do echo hi 2>&1;sleep 5;done &
This echoes out "hi" every 5 seconds like so:
[1] 30913
hi
$ hi
hi
hi
hi
Now when I run stty tostop:
$ stty tostop
$ date
Thu May 9 14:22:44 EDT 2013
$ date
Thu May 9 14:23:52 EDT 2013
The trouble with this approach is that the other process is stopped:
$ jobs
[1]+ Stopped while [ 1 ]; do
echo hi 2>&1; sleep 5;
done
The trouble with this approach is that stty -tostop didn't resume the process, just the setting of my stty stating that STDOUT is allowed again. So I had to resume my process manually:
$ stty -tostop
$ jobs
[1]+ Stopped while [ 1 ]; do
echo hi 2>&1; sleep 5;
done
$ fg
while [ 1 ]; do
echo hi 2>&1; sleep 5;
done
hi
^Z
[1]+ Stopped while [ 1 ]; do
echo hi 2>&1; sleep 5;
done
$ bg
[1]+ while [ 1 ]; do
echo hi 2>&1; sleep 5;
done &
$ hi
hi
hi
hi
hi
The above shows my running stty -tostop, then running the command fg to foreground the while ... process that was polluting my STDOUT, then Ctrl+Z, to stop the while ... process, then use the background command, bg.
Additional Ideas
Check out the suggestions tools on these U&L Q&As
There are extensive lists of tools and possible paths for you to try out as alternatives to screen. Perhaps use tmux or reconnect the processes that are polluting your STDOUT to another terminal using reptyr.