int sel = int.Parse(0+dataGridView2.CurrentRow.Cells["invoice_ID"].Value.ToString());
string sql = "DELETE FROM invoices WHERE invoice_id="+ sel +"";
DBConnection myCon = new DBConnection();
//mycon.EditeValues(sql) has all the sqldata reader,executenonQuery cmd
the error's arrow points out to the first line which is "int sel............".
As Ketsuekiame said if you're invoice is alph-numeric (letters and numbers) you can't parse it into an int.
Try taking the int.parse and .ToString() off the first line and adding (int)before the name dataGridView2 (that will also only work if the cell doesn't contain letters but it means you're not converting it to a string before trying to store it in an int).