In alternative embodiments, provided are non-natural or genetically engineered vinylisomerase-dehydratase enzymes, including alkenol dehydratases, linalool dehydratases and crotyl alcohol dehydratases. In alternative embodiments, provided are non-natural or genetically engineered polypeptides having an activity comprising, for example, a vinylisomerase-dehydratase, an alkenol dehydratase, a linalool dehydratase and/or a crotyl alcohol dehydratase activity, or a combination thereof. In alternative embodiments, also provided are non-natural or genetically engineered nucleic acids (polynucleotides) encoding polypeptides described herein, expression or cloning vehicles comprising or having contained therein nucleic acids as described herein, and non-natural or genetically engineered cells comprising or having contained therein nucleic acids as described herein. In alternative embodiments, also provided are methods for making various organic compounds, including methyl vinyl carbinol and butadiene.