In contrast to full-blown emotions, storytelling speech entails a particular speaking style that contains subtle expressive nuances of which little is known. In the present work, we study the role of prosody and voice quality while searching for cross-linguistic acoustic similarities in two categories of storytelling speech that are defined by their lexical components: the descriptive mode and sentences that specify a character intervention, together with a third neutral category (perceptually validated as reference). The study addresses four narrators using four different European languages (English, French, German and Spanish) expressing the same story. After conducting several statistical and discriminant analyses, we find that all narrators under analysis exploit some acoustic parameters in a similar way to differentiate among the analysed storytelling categories. Specifically, we observe that three prosodic features (mean fundamental frequency, mean intensity and number of silent pauses) and two voice quality parameters (mean Harmonic-to-Noise Ratio and Maxima Dispersion Quotient) explain a relatively similar proportion of the variance among storytelling categories in all languages. Moreover, the classification results obtained from the discriminant analysis are comparable for the three considered storytelling categories across languages.