Context : The high star formation rates of luminous infrared galaxies ( LIRGs ) make them ideal places for core-collapse supernova ( CCSN ) searches . Massive star formation can often be found in coexistence with an active galactic nucleus ( AGN ) , contributing jointly to the energy source of LIRGs . At radio frequencies , free from dust extinction , it is possible to detect compact components within the innermost LIRG nuclear regions , such as SNe and SN remnants , as well as AGN buried deep in the LIRG nuclei . Aims : Our study of the LIRG IC 883 aims at : ( i ) investigating the parsec-scale radio structure of the ( circum- ) nuclear regions of IC 883 ; ( ii ) detecting at radio frequencies the two recently reported circumnuclear SNe 2010cu and 2011hi , which were discovered by near-IR ( NIR ) adaptive optics observations of IC 883 ; and ( iii ) further investigating the nature of SN 2011hi at NIR wavelengths . Methods : We used the e-EVN at 5 GHz , and e-MERLIN at 6.9 GHz , to observe contemporaneously the LIRG IC 883 at high angular-resolution ( from tens to hundreds of milliarcsec ) and with high sensitivity ( < 70 \mu Jy ) , complemented by archival VLBI data at 5 and 8.4 GHz . We also used the Gemini-North telescope to obtain late-time JHK photometry for SN 2011hi . Results : The circumnuclear regions traced by e-MERLIN at 6.9 GHz have an extension of \sim 1 kpc , at a position angle of 130° , and show a striking double-sided structure , which very likely corresponds to a warped rotating ring , in agreement with previous studies . Our e-EVN observations at 5 GHz and complementary archival VLBI data at 5 GHz and 8.4 GHz , reveal the presence of various milliarcsec compact components in the nucleus of IC 883 . A single compact source , an AGN candidate , dominates the emission at both nuclear and circumnuclear scales , as imaged with the e-EVN and e-MERLIN , respectively . The other milliarcsec components are very suggestive of ongoing nuclear CCSN activity . Our e-EVN observations also resulted in upper limits to the radio luminosity of the two SNe in IC 883 recently discovered at NIR wavelengths . We refine the classification of SN 2011hi as a Type IIP SN according to our latest Gemini-North epoch from 2012 , in agreement with a low-luminosity radio SN nature . We estimate a CCSN rate lower limit of 1.1 _ { -0.6 } ^ { +1.3 } yr ^ { -1 } for the entire galaxy , based on three nuclear radio SNe and the circumnuclear SNe 2010cu and 2011hi . Conclusions :