I've found using software serial with an Attiny84's internal oscillator works just fine, especially at lower baud rates (e.g. 9600). I use the arduino-tiny cores on code.google
The symptoms you're having suggest a baud rate mismatch. Since it seems that you have it set to 9600 baud on both sides, my first guess is that the chip is actually running at 1 MHZ. Did you "Burn bootloader", i.e. flash the fuses to set the chip to run at 8 MHZ?
If my guess is wrong, then... well very curious. I'd maybe want to rule out the serial adapter as the problem. Do you have an Arduino etc with a hardware UART you could use to test the setup?