Due to James Joyce's conceptual and linguistic originality, the significance and complexity of his works, the research of his works and their translations have been ongoing in the West for well over half a century, but the humanities studies in Latvia for various reasons have paid comparatively little attention to it. Ulysses is one of the most significant works in the history of world literature, its translation is a true test of a translator's skill. Therefore, the work that the writer and translator Dzintars Sodums (1922-2008) invested in the Latvian translation of the novel has been estimated to be a significant contribution to the Latvian culture. This research describes Sodums' translation, analysing his solutions to the problems of translating style in one of the most stylistically unusual texts in the history of English and Irish literature - the 14th Episode of Ulysses, better known under the title of 'Oxen of the Sun'. The object of the research: solutions to the translation problems of pastiches and parodies in the Latvian translation of the 14th Episode of Joyce's novel Ulysses. The question of the research: what solutions did the Latvian translator Sodums employ to address translation problems in his translation of Joyce's pastiches and parodies, and what were the resulting effects, when viewed from the perspective of translational stylistics? This research integrates various scientific approaches to the analysis of translations with the theories of literary studies that focuses on the reader's perception and questions of stylistics. Apart from the criteria that apply specifically to the translation of 'Oxen of the Sun', the methodology of the research can be used for the analysis of translational stylistics of various works of literature in order to classify the translation shifts in contrast to the source text and to determine their stylistic effect. The conclusions of this doctoral thesis encompass both the theoretical questions (the suitability of various theoretical approaches of the translation studies in examining the translational stylistics; the definition and distinction of parody and pastiche; the role of cognitive poetics and receptive aesthetics in the examination of translational stylistics), as well as practical questions of translation studies, linguistics and literary studies (the suitability of proposals of translation and literary studies for the study of translational stylistics of the 14th Episode of Ulysses; the possible concepts for translation of this Episode, the applicable criteria for analysing translational stylistics of this Episode, determined by the specificity of the text; the stylistic changes specific to the Latvian translation when compared to the source text). Some of the terminology used in this doctoral thesis has never been used in the Latvian language before because they have been constructed for the purposes of this research. Therefore, this study may be utilized to enlarge the terminology of the translation studies in the Latvian language.