The invention provides a polymer composition comprising from 50 wt % to 99.9 wt % polymer, from 0.1 wt % to 10 wt % nanocellulose as a first nucleating agent, and from 0.01 wt % to 5 wt % of a second nucleating agent. In some embodiments, the polymer is polylactide, the first nucleating agent is lignin-containing nanocellulose, and the second nucleating agent is a sulfur-containing, oxygenated aromatic molecule. The oxygenated aromatic molecule may be an aromatic sulfonic acid or salt, such as dimethyl 5-sulfoisophthalate. In other embodiments, the sulfur-containing, oxygenated aromatic molecule is lignosulfonic acid. Other variations provide a polymer composition comprising polymer, lignin-containing nanocellulose as a dispersing agent, and additives selected from nucleating agents, compatibilizers, plasticizers, fillers, antioxidants, colorants, or flame retardants. Other variations provide a polymer nucleating agent comprising lignin-containing nanocellulose and a sulfur-containing, oxygenated aromatic molecule. This may be a nucleating agent for polylactide, polycaprolactone, polyhydroxybutyrate, polyethylene, or polypropylene, for example.