Read 8 serial ports at the same time with an Attiny
This is possible... but hard. 

The idea is to sample all of the GPIO pins at least 2x the rate of the serial bitstream and use software to decode any data that comes in.

You probably want to do the sampling in a timer-driver ISR and have it store the sampled level bytes into a circular buffer. Then the foreground process can pull sample bytes out of the buffer and decode the levels into data bits and bytes.

If you can assign all the serial pins to the same port (like PORTA on the ATTINY84), then you can very efficiently grab all the levels at once with a single IN instruction and efficiently store them in the target buffer as a single byte. 

If you can sample at 16x the data rate then you can even do edge sync like a good hardware USART does....



Of course even at 20Mhz, this is a lot of work for a little ATTINY so you will be limited to the max baud, max duty cycle, and max processing you will be able to do before you run out of steam.