Oscillator Strength and Absorption Intensity in TDDFT
I'll address the last part of your question. I think the first part

What formulae relates the transition dipole moments, the oscillator
strength and the observed absorption relative intensity?

of your question could stand on its own.
The oscillator strength is connected to the transition dipole moment vector via
$$
f_{if} = \frac{2}{3}\omega_{if}|\vec \mu_{if}|^2
$$
in atomic units,i.e. $m_e=\hbar =1$, $\hbar \omega_{if}=(E_f-E_i)$. The equation in SI units can be found on Wikipedia. $i,f$ stand for the initial and final electronic state involved in the transition.
For spontaneous emission, you have to multiply $f_{if}$ by an additional factor of $\omega_{if}^2$ since spontaneous emission is proportional to $\omega_{if}^3|\mu_{if}|^2$.
The oscillator strength is already a dimensionless relative quantity and the ratio of different oscillator strengths should correspond to the ratio's in an absorption spectrum measurement. Just normalize everything by the highest value if you are going for a  plot that is comparable with a relative intensities plot where the peaks are also  normalized .
It is important to note that the calculation only describes a purely electronic transition and yields only a single line at the energy difference of the involved adiabatic electronic states. The result of a real measurement is not a single line and includes many effects that are not described by a simple excited electronic states calculation.
But the calculation gives you an estimate where the center of the peaks should be and how intense they should be. A simple TD-DFT calculation does not give you information about the detailed lineshape. The lineshape is typically assumed to have some form and then added by broadening a stick spectrum based on the oscillator strenghts with a spectral lineshape function. The width of the lineshape function is then adjusted to match the experimental measurement manually.  Common lineshape functions are here.