I tried to use RestSharp from VSPackage and it works. My steps to add RestSharp:
Add RestSharp by NuGet in a project where I will use it. To do this, right-click on the project in Solution Explorer and selecting the “Manage NuGet Packages…”, find RestSharp and press Install button.
Write test code in this project:
var test = new RestSharp.RestClient("http://test.com");
Logger.Log(Category.Info, "Test {0}", test.BaseUrl);
Add RestSharp by NuGet in the installer project. Similarly paragraph 1. I use the VSIX Deployment Package. To set the necessary assembly just need to add a reference to assembly in the VSIX Deployment Package. This makes the “Manage NuGet Packages…” command. When you create a VSPackage by VS Wizard, the main project of VSPackage is VSIX Deployment Package.
If you use another method of installation your VS extension (for example, MSI installer), you need to explicitly add RestSharp.dll to our installation package.
As a result, I got line "Test http://test.com" in the log.
Most likely in your case, that RestSharp.dll been not installed and therefore VS is not finding RestSharp.dll when loading your module. Or the fully qualified name of installed RestSharp assembly is different from the fully qualified name assembly in References of project. To see this check out whether RestSharp.dll file in folder of your extension (for VSPackage by default patch is "%LOCALAPPDATA%\MICROSOFT\VISUALSTUDIO\11.0EXP\EXTENSIONS\{YourCompanyName}\{YourProductName}\{YourProductVersion}\"). You can see the absolute path to your extension in the Modules window if run the extension under the debugger.
Edit: I just now noticed that the RestSharp assembly from NuGet has not a strong name. So the directory of installed extension and References of projects should contain the exact same assembly with a strong name, and everything will work fine.