Obs.: I'm considering that you have the ASI Loader and ScriptHookVDotNet installed. Case you didn't installed them yet, check this post.
Those issues are commonly related to problems with the ScripthookVDotNet (let's call it SHDotNet) plugin, basically what can happen is:
Issue #1: Outdated SHDotNet
Some mods may come with a unwanted copy of SHDotNet that can be outdated, if you try to use my mods with a outdated version of SHDotNet they may fail to load due to missing/renamed methods in the outdated version of SHDotNet, to check if this is your case you can open a SHDotNet LOG file and check for errors, the log file may look like:
In the LOG file search for the words "[ERROR] Caught fatal unhandled exception:" and you may find a error like this one:
"[11:27:46] [ERROR] Caught fatal unhandled exception:
System.MissingMethodException: Method not found: ..."
SOLUTION: Update your SHDotNet with latest version from official source (The ScriptHookVDotNet.zip link)
Issue #2: ASI Loader fails to load SHDotNet
If even with latest version of SHDotNet your mods menu still don't load it may be result of SHDotNet not even being loaded, to confirm this case open the asiloader LOG file and see the line that refers to the SHDotNet, if you find something like this:
Loading "...\Grand Theft Auto V\ScriptHookVDotNet.asi"
"ScriptHookVDotNet.asi" failed to load
SOLUTION: You need to check if your windows have the required windows packages installed and working, the packages are:
-Microsoft .NET Framework 4.5 (direct link)
-Microsoft .NET Framework 4.5.2 (direct link)
-Visual C++ Redistributable Package for Visual Studio 2013 (x64) (direct link)
-Visual C++ Redistributable for Visual Studio 2015 (x64) (direct link)
If you can't find the line with ScriptHookVDotNet word you not even have the ScriptHookVDotNet plugin installed :)
Issue #3: ScriptHookVDotNet.dll file in Scripts folder
I don't know why but the developers of SHDotNet didn't added a filter to ignore the SHDotNet .dll file in scripts folder, when the user paste the ScriptHookVDotNet.dll file in Scripts folder some of the mods may not work due to the SHDotNet trying to load "himself" as a script mod :)
SOLUTION: Remove the ScriptHookVDotNet.dll file from scripts folder and place it in the right place that is game root folder (gta5.exe folder)
Issue #4: Scripts not in scripts folder
SOLUTION: Make sure that the scripts (.net.dll files of the ZIP/,OIV package) are in the gta Scripts folder, otherwise the SHDotNet can't find and load them. My mods goes with a ZIP file with the structure that you can simple copy and paste in game root folder for easy installation.
Case you still have issues or other errors in log file, try to contact the developers in the official post of SHDotNet clicking here