Use Action or FUNC in dictionaries

this method for example is a setter so it receives as a parameter (double or string or int etc...) and return void.

That's the problem - a method accepting a double isn't applicable for Action<object>, because an Action<object> should be able to be invoked with any object reference as the argument.

You can use a lambda expression to cast and convert though:

myDict.Add("somestring", o => MethodAcceptingDouble((double) o));

You could even write a helper method to do it, although unfortunately due to limitations of type inference you need to specify the type argument explicitly.

static class Test
{
    static void Main()
    {
        var dictionary = new Dictionary<string, Action<object>>();
        AddAction<double>(dictionary, "somestring", SampleMethod);
    }

    static void AddAction<T>(Dictionary<string, Action<object>> dictionary,
                             string name,
                             Action<T> action)
    {
        dictionary.Add(name, arg => action((T) arg));
    }

    static void SampleMethod(double input)
    {
    }
}