Just ask about the name of the father directly, when you will ask, you can say: "подскажи пожалуйста, а как тебя звать по батюшке?" Or say like this: " подскажи пожалуйста твое отчество", and listen carefully. And it is better to write down what would you here.

For the last name you can simply ask: "Какая у Вас/тебя фамилия?" For the middle (father's) name: "Как Вас по отчеству?" or if you don't even know the first name: "Как Вас по имени-отчеству?" Above-mentioned "Как вас по батюшке?" is used only as a joke and never appropriate in any more or less formal context. Middle/father's name is not used when you are addressing a friend.

Generally we use a first name together with a father's name to show the respect to a person. Very often we do not use "ты" in that case and use "Вы". "Подскажите, как я могу к вам обращаться?", "Могу ли узнать ваше имя и отчество?", "Как я могу вас называть по имени и отчеству?" But this is more formal way to ask. It is also possible to ask your friend whom you call just by a first name. " (А) какое у тебя отчество?" (very informal way to ask)

If they are your friends, you don’t need to use their “father’s name”.

You may ask Tatyana: Татьяна, не подскажете,а какая у вас фамилия? And as for Oksana - Amir gave you the great answer! =) (как тебя звать по батюшке?) xD