The nutritional characteristics of fatty acid (FA) containing foods are strongly dependent on the FA’s chemical/morphological arrangements. Paradoxically the nutritional, health enhancing FA polyunsaturated fatty acids (PUFAs) are highly susceptible to oxidation into harmful toxic side products during food preparation and storage. Current analytical technologies are not effective in the facile characterization of both the morphological and chemical structures of PUFA domains within materials for monitoring the parameters affecting their oxidation and antioxidant efficacy. The present paper is a review of our work on the development and application of a proton low field NMR relaxation sensor (1H LF NMR) and signal to time domain (TD) spectra reconstruction for chemical and morphological characterization of PUFA-rich oils and their oil in water emulsions, for assessing their degree and susceptibility to oxidation and the efficacy of antioxidants. The NMR signals are energy relaxation signals generated by spin–lattice interactions (T1) and spin–spin interactions (T2). These signals are reconstructed into 1D (T1 or T2) and 2D graphics (T1 vs. T2) by an optimal primal-dual interior method using a convex objectives (PDCO) solver. This is a direct measurement on non-modified samples where the individual graph peaks correlate to structural domains within the bulk oil or its emulsions. The emulsions of this review include relatively complex PUFA-rich oleosome-oil bodies based on the aqueous extraction from linseed seeds with and without encapsulation of externally added oils such as fish oil. Potential applications are shown in identifying optimal health enhancing PUFA-rich food formulations with maximal stability against oxidation and the potential for on-line quality control during preparation and storage.