I'm looking for an API or other service with a taxonomy of occupations, skills and so forth in a structured or unstructured description.
Have you looked at Schema.org 's "Occupation"? This may correspond to what you need. It's not an API, but you can build (or someone might have) one which uses it.
US federal Standard Occupational Classification (SOC) sysem is a federal statistical standard used by federal agencies to classify workers into occupational categories for the purpose of collecting, calculating, or disseminating data. All workers are classified into one of 867 detailed occupations according to their occupational definition. To facilitate classification, detailed occupations are combined to form 459 broad occupations, 98 minor groups, and 23 major groups. Detailed occupations in the SOC with similar job duties, and in some cases skills, education, and/or training, are grouped together.