A detailed understanding of how the activity of a galactic nucleus regulates the growth of its host is still missing. To understand the activity and the types of accretion of supermassive black holes in different hosts, it is essential to study radio-optical properties of a large sample of extragalactic sources. In particular, we aim at studying the radio spectral index trends across the optical emission line diagnostic diagrams to search for potential (anti)correlations. To this goal, we combine flux densities from the radio FIRST survey at 1.4GHz (with the flux density range 10mJy<=F1.4<=1000mJy for 209 SDSS sources at intermediate redshift (0.04<=z<=0.4) with the Effelsberg radiotelescope measurements at 4.85GHz and 10.45GHz. The information about the optical emission-line ratios is obtained from the SDSS-DR7 catalogue. Using the Effelsberg data, we were able to infer the two-point radio spectral index distributions for star-forming galaxies, composite galaxies (with a combined contribution to the line emission from the star-formation and AGN activity), Seyferts, and low ionization narrow emission region (LINER) galaxies. While studying the distribution of steep, flat, and inverted sources across optical diagnostic diagrams, we found three distinct classes of radio emitters for our sample: (i) sources with steep radio index, high ionization ratio and high radio loudness, (ii) sources with flat radio index, lower ionization ratio and intermediate radio loudness, (iii) sources with inverted radio index, low ionization ratio and low radio loudness. The classes (i), (ii), (iii) cluster mainly along the transition from Seyfert to LINER sources in the BPT diagram. We interpret these groups as a result of the recurrent nuclear-jet activity.