Aims: We present a study of the Be/X-ray binary system V 0332+53 with the main goal of characterizing its behaviour mainly during the intermediate-luminosity X-ray event in 2008. In addition, we aim to contribute to the understanding of the behaviour of the donor companion by including optical data from our dedicated campaign starting in 2006. Methods: V 0332+53 was observed by RXTE and Swift during the decay of the intermediate-luminosity X-ray outburst of 2008, and with Suzaku before the rising of the third normal outburst of the 2010 series. In addition, we present recent data from the Spanish ground-based astronomical observatories of El Teide (Tenerife), Roque de los Muchachos (La Palma), and Sierra Nevada (Granada), and since 2006 from the Turkish TÜBİTAK National Observatory (Antalya). We have performed temporal analyses to investigate the transient behaviour of this system during several outbursts. Results: Our optical study revealed that continuous mass ejection episodes from the Be star have been taking place since 2006 and another is currently ongoing. The broad-band 1-60 keV X-ray spectrum of the neutron star during the decay of the 2008 outburst was well fitted with standard phenomenological models that were enhanced by an absorption feature of unknown origin at about 10 keV and a narrow iron K-alpha fluorescence line at 6.4 keV. For the first time in V 0332+53 we tentatively see an increase in the cyclotron line energy with increasing flux (although further and more sensitive observations are needed to confirm this). The fast aperiodic variability shows a quasi-periodic oscillation (QPO) at 227 ± 9 mHz only during the lowest luminosities, which might indicate that the inner regions surrounding the magnetosphere are more visible during the lowest flux states.