Altered metabolism of lipids is a key factor in many diseases including cancer. Therefore, investigations into the impact of unsaturated and saturated fatty acids (FAs) on human body homeostasis are crucial for understanding the development of lifestyle diseases. In this paper, we focus on the impact of palmitic (PA), linoleic (LA), and eicosapentaenoic (EPA) acids on human colon normal (CCD-18 Co) and cancer (Caco-2) single cells using Raman imaging and spectroscopy. The label-free nature of Raman imaging allowed us to evaluate FAs dynamics without modifying endogenous cellular metabolism. Thanks to the ability of Raman imaging to visualize single-cell substructures, we have analyzed the changes in chemical composition of endoplasmic reticulum (ER), mitochondria, lipid droplets (LDs), and nucleus upon FA supplementation. Analysis of Raman band intensity ratios typical for lipids, proteins, and nucleic acids (I1656/I1444, I1444/I1256, I1444/I750, I1304/I1256) proved that, using Raman mapping, we can observe the metabolic pathways of FAs in ER, which is responsible for the uptake of exogenous FAs, de novo synthesis, elongation, and desaturation of FAs, in mitochondria responsible for energy production via FA oxidation, in LDs specialized in cellular fat storage, and in the nucleus, where FAs are transported via fatty-acid-binding proteins, biomarkers of human colon cancerogenesis. Analysis for membranes showed that the uptake of FAs effectively changed the chemical composition of this organelle, and the strongest effect was noticed for LA. The spectroscopy studies have been completed using XTT tests, which showed that the addition of LA or EPA for Caco-2 cells decreases their viability with a stronger effect observed for LA and the opposite effect observed for PA. For normal cells, CCD-18 Co supplementation using LA or EPA stimulated cells for growing, while PA had the opposite impact.