Data Loader v38 (Winter 17)

As commented by Charles, v38.0.1 is now available:

DataLoader V38.0.1 fixed Oauth option missing issue caused by release script and a bug in field mapping UI after sorting by column names.

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Partial answer, to at least get you going until the missing OAuth authentication can be resurrected.

You will need to append your security token to the end of the password unless your current IP address is listed under Trusted IP Ranges.

Conversely, if the Organization has restricted IP addresses enabled you will only be able to login from those IP addresses and you won't need the security token.

I'll try pinging the Salesforce Docs team to see if they can clarify the confusing point in the Data Loader documentation.

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Caspars comment with the link to the Github project would be a good place to raise the missing OAuth issue.

Issue created by Mohith - New Version 38.0 of dataloader has oauth option missing

Randomly searching the projects code, it occurs to me that it will need to have access to the OAuth Client secret to get the flow started as the correct connected app. You can see this at line 86 of AuthenticationRunner. If the sfdc.oauth.clientsecret was missing from the config then you wouldn't even get the OAuth option.