Microstructured optical fibres (MOFs), also known as Photonic Crystal Fibres (PCFs) or Holey Fibres (HFs), play an important role in supercontinuum generation because of their high nonlinearity and ability to tailor the dispersion profile. Nowadays, studies have extended to the multimode environment to enhance spectral broadening by taking advantage of various intermodal nonlinear effects. Recently, it has been shown that these types of fibres can also be able to provide spatially cleaned output beams through a novel nonlinear spatial effect called Kerr-induced beam self-cleaning (KBSC), which makes these fibres suitable for a variety of multimode-based applications. In this paper, a full modal analysis of germanium (Ge)-doped graded-index multimode PCFs with different geometrical sizes is provided. The influence of fibre size on modal properties, such as effective refractive index, birefringence and dispersion, was investigated using the finite element method. It was found that the changes in the geometric parameters can significantly affect the modal properties and then the frequency generation and spectral broadening. Experimentally, high-efficiency frequency generation with different frequency detunings was obtained in a short length of each PCF by launching input pulses at 1064 nm pump wavelength. For longer fibre length and high input power, supercontinuum generation with improved broadening from visible to near IR by intermodal four-wave mixing and stimulated Raman scattering was observed in all PCFs. A study of the effect of input peak power, input polarization axis and fibre length on supercontinuum spectrum is presented. Experimental evidence of the KBSC effect as a function of various fibre and laser parameters is also reported. The evolution of spatial output beam pattern from higher-order mode to fundamental mode with low-peak-power self-cleaning threshold was observed for all the fibres by launching a 1064 nm pump laser with 1 ns pulse duration.