Help with converting a sting of chars to an int via toInt().

Welcome to the Forum, Emma. First, what terminates the input stream? Is it a newline character ('\n"), null ('\0'), of what? If it is always in a field of 6 characters, you might change:

void loop() {		
	
	if (Serial.available() > 0){

		if(CharIndex < 6){
			IncomingChar = Serial.read();
			IncomingStr[CharIndex] = IncomingChar;  //Save the char to our list
			CharIndex ++;
			IncomingStr[CharIndex] = 0;  //Insure the next place is cleared
		}

to

void loop() {		
	
	if (Serial.available() > 0){
            Serial.readBytesUntil('\n', incomingStr, 6);

This grabs everything and puts it in one place. Next, I would separate out the display info into it's own function, like:

void loop() {		
		
	if (Serial.available() > 0){
            Serial.readBytesUntil('\n', incomingStr, 6);
            ShowMeWhatArrived();
// more of your code...
}  // End of loop()

void ShowMeWhatArrived()
{
   incomingStr[5] = '\0';           // Make sure we can treat it as a string

   Serial.print("Direction: ");
   Serial.print(incomingStr[0]);
   Serial.print("Left-Right: ");
   Serial.print(incomingStr[1]);
   Serial.print("Magnitude: ");
   Serial.print(atoi(&incomingStr[2]));
}

Obviously I haven't tried this, but it should point you in the right direction. The only thing that may seem a little weird is the argument to atoi(). Think of the address-of operator (&) as saying: "Give me the memory address where I can find...". So, if incomingStr[] is located at memory address 1000, &incomingStr[2] fetches memory address 1002. The atoi() function then goes to that address, finds "135", and converts it from an ASCII character sequence to a 16-bit integer.