You should know that the previous episode with Suttungr, Odhinn is was rented as a farmhand to Suttungr brother, known as Bölverk. The contract stipulated that if the work was well done, this brother would request Suttungr to Odhinn a SIP of the Mead of poetry. But when asked this Suttungr, stubbornly refused. Odhinn then borrowed from brother (obviously a giant knowing magic) a magical auger named Rati whose 'mouth grignota stone' and Odhinn, turning into a snake, able to fit inside of Suttungr.
This stanza explains how Odhinn could enter without getting spot in the abode of Suttungr. The details of what it does immediately after is not known. Two hypotheses seem possible. Or well Odhinn after resuming human form, immediately enters the room where Gunnlodh was responsible for overseeing Mead, and it will negotiate directly with it. He will deceive her with fine words and false oaths. Or else he meets Suttungr and Gunnlodh. That Odhinn insists both here on the danger that he was running, it is clear that arguably Suttungr he was subjected to a kind of interrogation. According to what we know of Norse mythology, the behavior of the Giants with the gods was violently aggressive and Odhinn had to conceal from Suttungr was one of the Æsir. For this, it is possible that he had to swear on his ring he was not one of the Æsir. Of course, this oath was not sincere and this explains, according to Bellows (in stanza 108), the accusation of perjury in Odhinn in verse 110. It is even less likely that this episode is the only perjury he has committed. Indeed, it is not understood why, God or not, Suttungr has trusts this stranger who had entered his home break-ins. On the other hand, it is quite possible that Odhinn has explained his presence by a beautiful story of love desperate for Gunnlodh and that he has thus convinced Suttungr to life on condition that he married his daughter. He then did an oath on the ring to Gunnlodh also. This second interpretation has the advantage of being less likely that another but, it, it allows to understand the last verses of 110, as we shall see.
létumk rúms um fá
ok um grjót gnaga
yfir ok undir
stóðumk jötna vegir
svá hætta ek höfði til
 I let  the mouth of the gimlet
and gnaw through stone;
over and under
me stood the giants' paths (rocks):
thus I risked my head.