Getting parameter names and parameter types through reflection

I'm attempting to write a utility method which should be capable of executing any method. Consider this for example. I have a class with the following methods:

ClassA
   void Method1 (int a)
   void Method2 (int b, string s, long l)
   Object Method3 (string a, Object o)
   List<string> Method4 (double d, List<string> sList)

Now, in a different class, I have a method execute

ClassB
   void execute (string methodName, Map<string, object> params)

methodName will contain the required method's name (Method1/Method2/Method3/Method4) and params will have the parameters to be passed into the method. params will be a dictionary object like these for Method1 to Method4 respectively:

<Key>                     <Value>
"int"                     1

Or

"int"                     2
"string"                  "test"
"long"                    1234567896557

Or

"string"                  "abc"
"object"                  someClassObject

Or

"double"                  456.764
"List<string,string>"     someListObject

I know we can get the class and the methods through reflection, but is it possible to get the parameters to those methods? Along with the methods, I need to know what parameters (types and values) need to be passed into that method, so that I can lookup the params dictionary object and pass the correct parameters into the method. I have heard about paranamer, but want to know if this is possible without any external jars?