My grand grandfather was Meškauskas, who left Lithuania for the USA right before or after 1900 and lived there for more than 20 years. He may have had another family there.
As the commentator said, Meszkauskas, 'sz' pronounced as [sh], is now spelled as Meškauskas, but in old documents you will only find the 'sz' spelling (because of historical reasons).
Tonaitis is a Lithuanian surname, although rare. Tonaiciuke is not a surname, it is a diminutive word from Tonaitis, meaning something like 'a little girl of Tonaitis', so Tonaiciuke must have been either a daughter or a sister of Tonaitis, or a young unmarried female member of the Tonaitis' family. The female name equivalent for Tonaitis would be Tonaityte (for unmarried), or Tonaitiene (for married women). As I mentioned before, it is highly unlikely that a married woman would be referred to as Tonaiciuke. Besides, it is also highly unlikely that this diminutive form was used by someone from West or North West Lithuania, unless dictated by somebody else.
Further,Stanaitis and Sakalauskas are quite frequent surnames and up to this date they are spelled like this. As for Nauyokas, this is an anglicized version of the Lithuanian 'Naujokas', as 'j' is pronounced as [y] as in 'yet'. The female surname for Naujokas would be Naujokaite(for unmarried women) and Naujokiene (for married).
Last, Waraikiute. As it was mentioned in the previous reply, W is now spelled as 'V', but in old documents you will only find W spelling for V, as in case of 'sz' and 'š'. Unfortunately, there are no such surnames as 'Varaikiute' or 'Varaikius/ Varaikis' in Lithuanian. However, there are very similar surnames 'Vareikis' and 'Vareika', which, I guess, might be the surnames you are looking for. So, 'Vareikis' for men, 'Vareikyte' for unmarried women, 'Vareikiene' for married women; and 'Vareika' for men, 'Vareikaite' for unmarried women, 'Vareikiene' for married women.
I hope, this helps.