ODP.NET Como passar array de strings para um procedimento Oracle Stored?

Eu não usei o recurso udtType no ODP.NET, então não tenho certeza de como atingir seu objetivo com isso. No entanto, para passar um array de string você não precisa dele.

Como a documentação que você anexou, você precisa criar um pacote que contenha seu procedimento armazenado e use uma matriz associativa (não VARRAY) como parâmetro de entrada.

Por exemplo:

-- Create the table
CREATE TABLE TBLTEST (testID NUMBER, name VARCHAR2(50));

CREATE SEQUENCE seq_test
    MINVALUE 1
    START WITH 1
    INCREMENT BY 1
    NOCACHE;

CREATE OR REPLACE PACKAGE pkgTestArrayBinding
AS 
    -- Define an local scope associative array type called T_ASSOCIATIVE_ARRAY and make it as the type of input parameter
    TYPE T_ASSOCIATIVE_ARRAY IS TABLE OF VARCHAR(50) INDEX BY PLS_INTEGER;
    PROCEDURE TestArrayBinding(
        Param1 IN T_ASSOCIATIVE_ARRAY,
        Param2 IN T_ASSOCIATIVE_ARRAY);
END pkgTestArrayBinding;
/

CREATE OR REPLACE PACKAGE BODY pkgTestArrayBinding
AS
    PROCEDURE TestArrayBinding(
        Param1 IN  T_ASSOCIATIVE_ARRAY,
        Param2 IN  T_ASSOCIATIVE_ARRAY)
    AS
    BEGIN
        -- for all loop to insert them in a batch
        FORALL indx IN 1..Param1.COUNT
            INSERT INTO tblTest VALUES(seq_test.nextval, Param1(indx));

        FORALL indx IN 1..Param2.COUNT
            INSERT INTO tblTest VALUES(seq_test.nextval, Param2(indx));
    END TestArrayBinding;
END pkgTestArrayBinding;
/

Agora, execute este código, coloque sua própria string de conexão.

namespace Con1
{
    using System;
    using System.Data;

    using Oracle.DataAccess.Client;

    /// <summary>
    /// The program.
    /// </summary>
    internal class Program
    {
        #region Methods

        /// <summary>
        /// The main.
        /// </summary>
        private static void Main()
        {
            var con = new OracleConnection { ConnectionString = "User Id=usr;Password=pass;Data Source=XE" };

            con.Open();
            Console.WriteLine("Connected to Oracle" + con.ServerVersion);

            // create command to run your package
            var cmd = new OracleCommand("BEGIN pkgTestArrayBinding.TestArrayBinding(:Param1, :Param2); END;", con);

            var param1 = cmd.Parameters.Add("Param1", OracleDbType.Varchar2);
            var param2 = cmd.Parameters.Add("Param2", OracleDbType.Varchar2);

            param1.Direction = ParameterDirection.Input;
            param2.Direction = ParameterDirection.Input;

            // Specify that we are binding PL/SQL Associative Array
            param1.CollectionType = OracleCollectionType.PLSQLAssociativeArray;
            param2.CollectionType = OracleCollectionType.PLSQLAssociativeArray;

            // Setup the values for PL/SQL Associative Array
            param1.Value = new[] { "First Element", "Second Element ", "Third Element_" };
            param2.Value = new[] { "Fourth Element", "Fifth Element ", "Sixth Element " };

            // Specify the maximum number of elements in the PL/SQL Associative Array
            // this should be your array size of your parameter Value.
            param1.Size = 3;
            param2.Size = 3;

            // Setup the ArrayBindSize for each elment in the array, 
            // it should be bigger than the original length of element to avoid truncation
            param1.ArrayBindSize = new[] { 13, 14, 13 };

            // Setup the ArrayBindSize for Param2
            param2.ArrayBindSize = new[] { 20, 20, 20 };

            // execute the cmd
            cmd.ExecuteNonQuery();

            // I am lazy to query the database table here, but you should get you data now.
            // watch what happened to element "Third Element_"

            // Close and Dispose OracleConnection object
            con.Close();
            con.Dispose();
            Console.WriteLine("Disconnected");
        }

        #endregion
    }
}