We report channel and strain engineering of self-organized, gate-stacking heterostructures comprising Ge-nanosphere gate/SiO2/SiGe-channels. An exquisitely-controlled dynamic balance between the concentrations of oxygen, Si, and Ge interstitials was effectively exploited to simultaneously create these heterostructures in a single oxidation step. Process-controlled tunability of the channel length (5-95 nm diameters for the Ge-nanospheres), gate oxide thickness (2.5-4.8 nm), as well as crystal orientation, chemical composition and strain engineering of the SiGe-channel was achieved. Single-crystalline (100) Si1-xGex shells with Ge content as high as ×= 0.85 and with a compressive strain of 3%, as well as (110) Si1-xGex shells with Ge content of x = 0.35 and corresponding compressive strain of 1.5% were achieved. For each crystal orientation, our high Ge-content, highly-stressed SiGe shells feature a high degree of crystallinity and thus, provide a core 'building block' required for the fabrication of Ge-based MOS devices.