Abstract Background Oleaginous yeasts are promising microbial platforms for sustainable, bio-based production of biofuels and oleochemical building blocks. Bio-based residues provide sustainable and cost-effective carbon sources for fermentative yeast oil production without land-use change. Considering the regional abundancy of different waste streams, we chose complex biomass residue streams of marine origin; macroalgae hydrolysate, and terrestrial origin; wheat straw hydrolysate in the presence, and absence of corn steep liquor as a complex nitrogen source. We investigated the biomass and lipid yields of an array of well-described oleaginous yeasts; R. glutinis, T. asahii, R. mucilaginosa, R. toruloides, C. oleaginosus growing on these hydrolysates. Furthermore, their sugar utilization, fatty acid profile, and inhibitory effect of the hydrolysates on yeast growth were compared. For correlative reference, we initially performed comparative growth experiments for the strains on individual monomeric sugars separately. Each of these monomeric sugars was a dominant carbon source in the complex biomass hydrolysates evaluated in this study. In addition, we evaluated N-acetylglucosamine, the monomeric building block of chitin, as a low-cost nitrogen and carbon source in yeast fermentation. Results C. oleaginosus provided the highest biomass and lipid yields. In the wheat straw and brown algae hydrolysates, this yeast strain gained 7.5 g/L and 3.8 g/L lipids, respectively. Cultivation in algae hydrolysate resulted in a higher level of unsaturated fatty acids in the lipids accumulated by all yeast strains. R. toruloides and C. oleaginosus were able to effectively co-utilize mannitol, glucose, and xylose. Growth rates on wheat straw hydrolysate were enhanced in presence of corn steep liquor. Conclusions Among the yeast strains investigated in this study, C. oleaginosus proved to be the most versatile strain in terms of substrate utilization, productivity, and tolerance in the complex media. Various fatty acid profiles obtained on each substrate encourage the manipulation of culture conditions to achieve the desired fatty acid composition for each application. This could be accomplished by combining the element of carbon source with other formerly studied factors such as temperature and oxygen. Moreover, corn steep liquor showed promise for enhancement of growth in the oleaginous strains provided that carbon substrate is available.