Hello Bernardine Woida Tucker,
Yesterday I checked the protestant-Lutheran church records to find the birth of your ancestors Friedrich WOIDA on September 18,1848 in Hanover, but he was not in this file. Do you know if he was protestant? There were no surname WOIDA in these files. I only found WOITAG, born 1859 and 1862, died 1861 in Hanover (Gartenkirche), but here also no data of a birth of 1848.
Today there are no people with the name WOIDA living in Hanover, but I found them in the area of Celle, Diepholz, Northeim and Vechta/Bremen. Maybe this will help you a little bit.
I checked Google Earth and the only town with the name "Hammer" is "Hammer an der Uecker", this belongs to the area fo Randow-Uecker in Mecklenburg-West Pomerania. So this could not be the town you are looking for, because it did not belonged to the Kingdom of Hanover. If you will find more hints I will be glad to help you.
Greetings from Germany,
Monika (Moehring)
www.genealogiemoehring.npage.de