Short answers, pulled from the story.
The England runestones are a group of about 30 carved stones in Scandinavia that record Viking Age voyages to England. Twenty-seven are in modern-day Sweden, with 17 clustered in the provinces around Lake Mälaren. There is also one in Norway, one in Schleswig, Germany, one in Scania, and one in Saint Paul's Cathedral in London.
The danegeld was a large silver payment made by Anglo-Saxon rulers to Scandinavian Vikings to stop raids on England during the 990s and early 11th century. Runestone U 344 at Yttergärde is the most notable example: it records that Ulf of Borresta collected the danegeld three times, in 991 with Skagul Toste, in 1012 with Thorkel the High, and in 1018 from Canute the Great.
The Thingmen were the elite bodyguard that Canute the Great kept after sending home most of the Vikings who helped him conquer England. Members of this assembly retinue are commemorated on several runestones, including Sö 160 at the church of Råby in Södermanland.
Runestone E 2, also known as Br E2, is a Viking Age runic inscription from the early 11th century found in Saint Paul's Cathedral in London. It is carved in Ringerike style on limestone and retains traces of dark blue and red pigment. The stone is now held at the Museum of London.
The Grinda Runestone, Sö 166 in Södermanland, commemorates a man named Guðvér who divided payment in England and attacked townships in Saxony. Omeljan Pritsak interprets the payment as part of the danegeld, and Erik Brate links the expedition to the one mentioned on the Berga Runestone.
The Nävelsjö runestone, Sm 101, is located at the estate of Nöbbelesholm in Småland, Sweden. It is unusual because it specifies the burial location of the man it commemorates: a father who died in England and was buried by his brother in Bath, Somerset.