Gordon/Taylor, para. 164:

"sín, sik, sér were used only reflexively, referring to the subject
of the sentence. Only in indirect speech put in the form of an
accus. and infin. could these pronouns be used of the object
(=subject in the original speech), as in Þorvaldr bað Gretti hafa
sik (i.e. Grettir) spakan `Thorvald told Grettir to keep quiet'.
Even in the accus. and infin. however the referrence was often to
the subject, as in goðin kváðu hann hafa vélt sik" --`the gods said
that he had deceived them' (presumably...). I'm not sure where this
last quote is from or what the context is; there's no reference to
it in the GT glossary; the nearest Google found was this, from
Völsunga saga:

1) kvað hann hafa vélt sik í tryggð `he (Gunnar) said that he
(Sigurd) had been unfaithful and deceived him (Gunnar)'.

Another exception to the above is impersonal verbs. Here the
reflexive pronouns can refer to the `logical subject' even if this
is expressed with an oblique case, as in the first `sín' in the
following example. The final `sik' though refers right back to the
original subject.

2) En at skilnaði þá mælir Útgarðaloki till Þórs ok spyrr hvernig
honum þykkir ferð sín orðin, eða hvárt hann hefir hitt ríkara mann
nokkvorn en sik.

`And at their parting, Utgardaloki speaks to Thor and asks [him] how
he thinks his (=Thor's) journey has gone, and whether he has [ever]
met a mightier man than him' (=Utgardaloki).

If I've got this right, `þykkja' can apparently behave in a similar
way with regard to reflexives even where the `grammatical subject'
is expicit and the `logical subject' not; this from Völsunga saga:

3) þykkja þeir fyrr gert hafa sakar við sik
`he thinks (or they seem to him) to have given him cause enough [for

The next example, also from Völsunga saga, seems to break the rule
of referring to the subject. Maybe it's due to the fact
that `minna' also operates as an impersonal verb, mik minnir e-s `I
remember, I think of s-thing':

4) hann minnir opt Sigmund á sína harma
`he (=Sinfjotli) often reminds Sigmund of his (Sigmund's) grievances'

Finally, here is an example from Yngvars saga víðförla which I think
might be ambiguous as far as the grammar goes, but depend on context:

5) ok lét jarl sér þó þykkja betra, ef hann léti eigi nauðmág sinn
sitja jafnhátt sér í Svíþjóð.
`and the jarl makes it known however that he would prefer it if he
(=King Eirik of Sweden) didn't let his (=Eirik's) self-appointed son-
in-law sit as high as himself (= Eirik) in Sweden.

(nauðmág `self-appointed son-in-law', as Edwards and Pálsson render
it, or more literally `son-in-law by force', refers to the man who
stole the king's daughter from her original husband, that is from
the husband the king approved of.)

Llama Nom