Ok, let's concretely talk about intermodulation effects:

If a microcontroller runs, it's not only the oscillator frequency and its harmonics, which must be taken into consideration. You will also see lots of other frequencies, which tend to smear to quasi continuous spectrum at very high frequencies. But what is often overlooked is, that due to the internal frequency dividing in order to make a machine cycle to last for 12 oscillation periods, ground noise will contain frequencies which are even lower than crystal frequency, concretely spoken frequencies of crystal frequency divided by 12 and its harmonics.

This can easily be seen in the following snippet of typical RF-emssion spectrum plot of a 87C51 running at 12MHz:



I have labelled the two stronger spikes at 36MHz and 48MHz. From this you can see, that there's this much finer spacing of spectrum lines, namely of 1MHz.

Now let's calculate what actual frequency will make problems:

Original poster told, that his reciever crystal is 27.175MHz. As he will use an intermediate frequency of 455kHz, then his sender will emit a frequency of 27.175MHz + 455kHz = 27.630MHz.

And what is the micro 'emitting' in this range?
11.0592MHz / 12 x 30 = 27.648MHz, which is only 0.018MHz away from the sender frequency of 27.630MHz. Now take into consideration some unavoidable tolerances of oscillation frequencies, then it's very probable, that he 'hits' the tuning frequency even better.

So, the original poster has selected the crystal frequency of reciever (and sender) rather unsuitedly. Nevertheless, switching to a proper grounding and shielding technique is still needed!!

Kai