Integrating smart heterogeneous objects, IoT devices, data sources, and software services to produce new business processes and functionalities continues to attract considerable attention from the research community due to its unraveled advantages, including reusability, adaptation, distribution, and pervasiveness. However, the exploitation of service-oriented computing technologies (e.g., SOC, SOA, and microservice architectures) by people with special needs is underexplored and often overlooked. Furthermore, the existing challenges in this area are yet to be identified clearly. This research study presents a rigorous literature survey of the recent advances in service-oriented composition approaches and solutions for disabled people, their domains of application, and the major challenges, covering studies published between January 2010 and October 2022. To this end, we applied the systematic literature review (SLR) methodology to retrieve and collate only the articles presenting and discussing service composition solutions tailored to produce digitally accessible services for consumption by people who suffer from an impairment or loss of some physical or mental functions. We searched six renowned bibliographic databases, particularly IEEE Xplore, Web of Science, Springer Link, ACM Library, ScienceDirect, and Google Scholar, to synthesize a final pool of 38 related articles. Our survey contributes a comprehensive taxonomy of service composition solutions, techniques, and practices that are utilized to create assistive technologies and services. The seven-facet taxonomy helps researchers and practitioners to quickly understand and analyze the fundamental conceptualizations and characteristics of accessible service composition for people with disabilities. Key findings showed that services are fused to assist disabled persons to carry out their daily activities, mainly in smart homes and ambient intelligent environments. Despite the emergence of immersive technologies (e.g., wearable computing), user-service interactions are enabled primarily through tactile and speech modalities. Service descriptions mainly incorporate functional features (e.g., performance, latency, and cost) of service quality, largely ignoring accessibility features. Moreover, the outstanding research problems revolve around (1) the unavailability of assistive services datasets, (2) the underspecification of accessibility aspects of disabilities, (3) the weak adoption of accessible and universal design practices, (4) the abstraction of service composition approaches, and (5) the rare experimental testing of composition approaches with disabled users. We conclude our survey with a set of guidelines to realize effective assistive service composition in IoT and cloud environments. Researchers and practitioners are advised to create assistive services that support the social relationships of disabled users and model their accessibility needs as part of the quality of service (QoS). Moreover, they should exploit AI/ML models to address the evolving requirements of disabled users in their unique environments. Furthermore, weaknesses of service composition solutions and research challenges are exposed as notable opportunities for future research.