SQL Developer has different connection methods than SQL*Plus and Toad.
You could try downloading the Toad 16.0 beta version. This version lets you connect to the database without using an Oracle client at all. (You can actually do that in 15.1 also but it's not as convenient).
if you do that, keep version 15.1 installed. When you install the beta, it will copy settings from version 15.1, but then each version will have its own copy of settings.
We are close to the official 16.0 release, so this beta version is almost identical to what will become the official version.