Use the OnTextChanged event to detect when the text is changed.
To handle the keyboard actions you can use the OnKeyDown, OnKeyPress and OnKeyUp events.

Html.Obout(new OboutTextBox("txt1")
{
    Width = 200,
    ClientSideEvents = new OboutTextBoxClientSideEvents()
    {
        OnTextChanged = "onTextChanged",
        OnKeyDown = "onKeyDown",
        OnKeyPress = "onKeyPress",
        OnKeyUp = "onKeyUp"
    }
})