A combination of single-molecule spectroscopy and analysis with simulations is used to provide detailed information about the structural and dynamic properties of a fluorescent polymer MEH-PPV (poly[2-methoxy-5-(2′- ethylhexyloxy)-1,4-phenylenevinylene]) immersed in a nematic and smectic solvent. In nematic solvents, single-polymer molecules are oriented strongly along the solvent director, much more so than the solvent molecules, confirming Onsager's old prediction. The diffusion anisotropy parallel and perpendicular to the solvent director, however, is less than two, which is similar to that of a spherical colloid in a nematic solvent. In smectic solvents, there is a second orientation of the dissolved polymer perpendicular to the solvent director, which we hypothesize is caused by the polymer occupying the interlayer volume. The research discussed here emphasizes the importance of organization in complex fluids and suggests that the interplay of order on different length scales could be exploited to fabricate novel nanostructured materials.