Did the Vikings use the Elder Futhark?
Mostly no. By the Viking Age the row had been cut down to sixteen runes, the Younger Futhark, and that is what Viking-age stones are carved in. The twenty-four of the Elder Futhark belong to the centuries before, roughly 150 to 700.
Where this comes from
oldest description the Younger row of sixteen · in use by about AD 800
Both Norse rune poems describe the sixteen, not the twenty-four: the Norwegian in the thirteenth century, the Icelandic in the fifteenth. Where an elder rune had left the row, this site says so on its page, in the same words each time. The elder row is older than every poem printed here.
What the poems say
The two Norse poems remember the Viking row: sixteen stanzas each, ending on ýr. The Old English poem walks a different road, the futhorc, which grew instead of shrinking. All three are printed whole on the witness pages.