(1) Background: Migrant and refugee youth’s (MRY’s) sexual and reproductive health and rights (SRHRs) are a global health issue. MRY encounter adverse SRH experiences due to limited access to and knowledge of SRHRs services. Using a socioecological framework, this study examined the barriers affecting MRY’s SRHRs. (2) Methods: A cross-sectional study utilising a participatory action research design was used. A total of 87 MRY (ages 16–26, from 20 cultural groups within Greater Western Sydney, Australia) completed seventeen focus group discussions on their SRHRs experiences. The focus groups were co-facilitated by youth project liaisons to ensure their authenticity and validity. The data were analysed thematically and interpreted using socioecological theory. (3) Results: The findings identified socioecological barriers, a lack of awareness about and access to services, and sociocultural dissonance as leading to the under-implementation of SRHRs services. These barriers included cultural disconnects, language barriers, remote service locations, intergenerational cultural conflicts, and ineffective SRHRs services. The key themes identified included traditional and institutional stigma, lack of SRH education, reliance on social media for SRH information, and privacy concerns. (4) Conclusions: There is a limited consideration of MRY’s SRHRs and the impact of intergenerational discordance and stigma on MRY’s rights. The findings suggest the necessity for a collaborative SRHRs strategy and policy design that empowers MRY’s agency across multicultural contexts.