Genealogy /
Where in Poland is the town of Laka? [20]
Galicia was the part of Poland which fell under the Austrian rule in the time of the partitions. Out of all the £ąkas only one would have been in Galicia then:
£ąka - wieś w woj. podkarpackim, w pow. rzeszowskim, w gminie Trzebownisko
£ąka - a village in Podkarpackie region, Rzeszów district, Trzebownisko gmina
en.wikipedia.org/wiki/£ąka,_Subcarpathian_Voivodeship
This would go along nicely with your grandfather's name, which seems to be most frequent in the very area: moikrewni.pl/mapa/kompletny/tomaka.html
But the other part of the story (your grandmother) is more complicated.
Szwilisa could be Silesia - Śląsk. Then you have 4 £ąkas to choose from:
£ąka - wieś w woj. dolnośląskim, w pow. bolesławieckim, w gminie Bolesławiec
£ąka (Wiesau) - wieś w woj. opolskim, w pow. nyskim, w gminie Otmuchów
£ąka (Lenke) - wieś w woj. opolskim, w pow. oleskim, w gminie Zębowice
£ąka (Lonkau) - wieś w woj. śląskim, w pow. pszczyńskim, w gminie Pszczyna
Only the last two villages from my original list can be now skipped as they're located in what used to be West Pomerania, near the Baltic Sea.
Silesia was under the German rule so the name was probably Germanized back then. Might not be £ąka but something else. There's also a place in Estonia called Lauga.
Can't help you more now. Hope at least some of it makes sense.