There are many problems in your "code" (and although I don't like to use this expresson for what is human readable and I believe should be called "program"; here, it is really a code for me...) so I try to address only one at a time. You should take a similar approach, try solving one problem at a time. Also I would suggest you to use simulators to understand further what happens in the micorocontroller while running.
1.

The poor little micro does not understand "text", you have to send out binary values, or make a "text" to binary conversion (I think the first is easier). If you send out "text" like this, actually there is a 8-bit binary character (see ASCII) transmitted for each _digit_ and some extra characters at the end of each line.

To debug this, just put out on a port what you have received (and do nothing more).

What tool do you use to send out the serial stream?

2.
You should not wait in the interrupt routine while you receive 3 characters; rather, receive only one character at a time and keep a counter (or a pointer) for keeping track where are you in the received stream. Also, maybe later you should reconsider the "protocol" you are using to have some means for resynchronisation if one byte gets lost somehow.

3. The R4-R6 registers should be initialized at the beginning.

4. It is not the best idea to rely on timing of PWM in "main" while interrupts might jump in randomly; it would be better doing in timer interrupts. But for starting, if you won't sit in the serial interrupt for too long (waiting for the 3 characters), it perhaps might work... Do you have an oscilloscope to have a look at the outcoming PWM?

Jan Waclawek