Nano-onions are ellipsoidal or spherical particles consisting of a core surrounded by concentric shells of nanometre size. Nano-onions produced by self-assembly and colloidal techniques have different structures and compositions, and thus differ in the state of strains. The mismatch of the thermal expansion coefficients and lattice constants between neighbouring shells induces stress/strain fields in the core and shells, which in turn affect their physical/mechanical properties and/or the properties of the composites containing them. In this paper, the strains in embedded and free-standing nano-onions with uniform and non-uniform compositions are studied in detail. It is found that the strains in the nano-onions can be modified by adjusting their compositions and structures. The results are useful for the band structure engineering of semiconductor nano-onions.