Early Binding with Generics
You're working with delegates so the Action variable should be declared as Delegate. Please note that you need to enclose the type in square brackets as Delegate is a reserved word.
Don't use Dim in class-scoped variables, instead apply the access level.
Declare your arrays in a .net fashion. The type should be Object().
All non-public fields should be in lowerCamelCase.
There's no need to apply the Overloads modifier as you're not redeclaring any existing methods.


Apply all the fixes allows you to perform a dynamic invoke.



Public Class WorkItem

    Private action As [Delegate]
    Private args As Object()

    Public Sub [Set](action As Action)
        Me.SetArgs(action)
    End Sub

    Public Sub [Set](Of T)(action As Action(Of T), arg As T)
        Me.SetArgs(action, arg)
    End Sub

    Public Sub [Set](Of T1, T2)(action As Action(Of T1, T2), arg1 As T1, arg2 As T2)
        Me.SetArgs(action, arg1, arg2)
    End Sub

    Private Sub SetArgs(ByVal action As [Delegate], ParamArray args As Object())
        Me.action = action
        Me.args = args
    End Sub

    Public Sub Execute()
        Me.action.DynamicInvoke(Me.args)
    End Sub

End Class




Alternative solution

Another approach would be to wrap the delegate in a parameterless action.

Public Class WorkItem

    Private method As Action

    Public Sub [Set](Of T)(action As Action(Of T), arg As T)
        Me.method = New Action(Sub() action.Invoke(arg))
    End Sub

    Public Sub [Set](Of T1, T2)(action As Action(Of T1, T2), arg1 As T1, arg2 As T2)
        Me.method = New Action(Sub() action.Invoke(arg1, arg2))
    End Sub

    Public Sub [Set](Of T1, T2, T3)(action As Action(Of T1, T2, T3), arg1 As T1, arg2 As T2, arg3 As T3)
        Me.method = New Action(Sub() action.Invoke(arg1, arg2, arg3))
    End Sub

    Public Sub Execute()
        Me.method.Invoke()
    End Sub

End Class


For old compilers

Public Delegate Sub Action()
Public Delegate Sub Action(Of T)(ByVal obj As T)
Public Delegate Sub Action(Of T1, T2)(ByVal arg1 As T1, ByVal arg2 As T2)
Public Delegate Sub Action(Of T1, T2, T3)(ByVal arg1 As T1, ByVal arg2 As T2, ByVal arg3 As T3)

Public Class WorkItem

    Private Class Closure(Of T)

        Public action As Action(Of T)
        Public arg As T

        Public Sub Invoke()
            Me.action.Invoke(Me.arg)
        End Sub

    End Class

    Private Class Closure(Of T1, T2)

        Public action As Action(Of T1, T2)
        Public arg1 As T1
        Public arg2 As T2

        Public Sub Invoke()
            Me.action.Invoke(Me.arg1, Me.arg2)
        End Sub

    End Class

    Private Class Closure(Of T1, T2, T3)

        Public action As Action(Of T1, T2, T3)
        Public arg1 As T1
        Public arg2 As T2
        Public arg3 As T3

        Public Sub Invoke()
            Me.action.Invoke(Me.arg1, Me.arg2, Me.arg3)
        End Sub

    End Class

    Private method As Action

    Public Sub [Set](Of T)(ByVal action As Action(Of T), ByVal arg As T)
        Dim closure As New Closure(Of T)
        closure.action = action
        closure.arg = arg
        Me.method = New Action(AddressOf closure.Invoke)
    End Sub

    Public Sub [Set](Of T1, T2)(ByVal action As Action(Of T1, T2), ByVal arg1 As T1, ByVal arg2 As T2)
        Dim closure As New Closure(Of T1, T2)
        closure.action = action
        closure.arg1 = arg1
        closure.arg2 = arg2
        Me.method = New Action(AddressOf closure.Invoke)
    End Sub

    Public Sub [Set](Of T1, T2, T3)(ByVal action As Action(Of T1, T2, T3), ByVal arg1 As T1, ByVal arg2 As T2, ByVal arg3 As T3)
        Dim closure As New Closure(Of T1, T2, T3)
        closure.action = action
        closure.arg1 = arg1
        closure.arg2 = arg2
        closure.arg3 = arg3
        Me.method = New Action(AddressOf closure.Invoke)
    End Sub

    Public Sub Execute()
        Me.method.Invoke()
    End Sub

End Class