Which Vinaya has the least number of rules? According to Wikipedia, “Extant vinaya texts include those of the Theravada (the only one in Pali), the Kāśyapīya, the Mahāsāṃghika, the Mahīśāsaka, the Dharmaguptaka, the Sarvāstivāda and the Mūlasarvāstivāda.” Does anyone know which of these Vinayas has the least number of rules? 

According to Peter Harvey (Introduction to Buddhism, p. 290), the Theravadin Vinaya has 227 rules for male monastics, the Mula-Sarvastivadin has 258, and the Dharmaguptaka has 250, making the Theravadin the one with the least number of rules.

The Wikipedia article on Vinaya substantially agrees with this, but has 253 for the Mulasarvastivadin Vinaya. However, the Wikipedia articles for Mahasamghika and Sthavira (and elsewhere) also state that the Mahasamghika Vinaya has the least number of rules, citing Andrew Skilton, A Concise History of Buddhism, stating that the Mahasamghika Vinaya has 67 rules in the śaikṣa-dharma section, compared to 75 for the Theravadin (apparently referring to the 75 sekhiyavatta), which appears to contradict Harvey’s statement that the Theravadin Vinaya has the least number of rules.

Does anyone (1) have any insights concerning the relative number of rules in the Vinayas that can reconcile this apparent contradiction or (2) know where English translations of the non-Theravadin Vinayas may be found? I am still researching this question online so may end up answering my own question, but would like to hear any relevant information from others.
Of the extant Vinayas, the Mahasanghika has the least rules, if by "rules" you mean "patimokkha rules". 

As per your post, the difference is almost entirely in the number of sekhiya rules, which are essentially table manners and the like. Indeed, in the early sources the number "150" rules is mentioned, and I believe this means that patimokkha in the time of the Buddha did not include the sekhiya rules. So if we were to count the rules as per the "original" patimokkha, there would be almost no difference between the Vinayas.

The patimokkha rules, however, are only a small, albeit important, collection of rules. Throughout the Vinaya there are many minor and incidental rules and procedures. Since these often occur by way of permutations of factors for other rules, it is difficult to count them exactly, and I don't believe anyone has done so.

The fact that the Mahasanghika has fewer sekhiya rules has been misinterpreted to imply that the Mahasanghikas were lax in Vinaya, and that their Vinaya text is early. In fact, from this we can't really draw any conclusions about the Vinaya practice of the Mahasanghikas (since the details that differ deal with tiny matters of etiquette), nor about the historical development of the Vinaya texts (since in other aspects the Mahasanghika Vinaya appears later than the Theravada).