Organic microstructures attract much attention due to their unique properties originating from the design of their shape and optical parameters. In this work we discuss the linear, second- and third-order nonlinear optical effects in arrays and in individual organic microstructures composed by self-assembling technique and formed randomly on top of a solid substrate. The structures under study consist of micro-spheres, -hemispheres or -frustums made of red laser dye and reveal an intense fluorescence (FL) in the visible spectral range. Importantly, that due to a high value of the refractive index and confined geometry, such micro-structures support the excitation of whispering gallery modes (WGM), which brings about strong and spectrally-selected light localization. We show that an amplification of the nonlinear optical effects is observed for these structures as compared to a homogeneous dye film of similar composition. The obtained data are in agreement with the results of the FDTD calculations performed for the structures of different dimensions. Perspectives of application of such type of organic nonlinear microresonators in optical devices are discussed.