Priyanka Bhave

This plugin adds login/ logout link in the navigation menu according to the user login status and then redirect to page/link set by admin and on click of login link a popup will open.
Plugin features :
<ol>
<li>Add login/ logout link to the naviation menu.</li>
<li>On click of login link Create a popup to login to the site.</li>
<li>Create a setting page for the admin to set redirection link after loggin/ logout</li>
</ol>
Steps to set redirection link :
<ol>
<li>Open the dashboard.</li>
<li>Click on login/ logout link under the settings menu.</li>
<li>Select the page or enter link to redirect after login/ logout for admin or non-admin login/ logout.</li>
</ol>

WP login/out link with login popup

This plugin adds login/ logout link in the navigation menu accordinng to the user login status and then redirect to page/link set by admin.

Julio Potier

Grégory Viguier

With this plugin you can now add a real log in/logout item menu with autoswitch when user is logged in or not. 
Nonce token is present on logout item. 
2 titles, one for ‘log in’ and one for ‘logout’ can be set up. 
Also, you can set the redirecion page you want, just awesome.

Login Logout Menu

This plugin (still) works great.

However be aware that it's not compatible with PHP 8 or newer, the latest PHP version this plugin will work with is 7.4. This is due to its use of create_function, which has been deprecated since PHP 7.2 and removed as of PHP 8. This should be replaced with an anonymous function, which is easy enough. But I haven't tested this myself, so I don't know if that's the only incompatibility with PHP 8+.

Works great, but...

You can now add a correct login & logout link in your WP menus.

WP login/out link with login popup vs Login Logout Menu