The View of St. Thomas Aquinas
I will confine my answer to St. Thomas Aquinas' view, and I will divide it into two parts: first whether demons such as Satan do in fact love, and secondly whether they can love. All quotes are from Aquinas.
Perhaps other users can represent a non-Catholic or non-Thomistic view given the Meta discussion which promotes the practice of working on overview questions collaboratively (link).
Do Demons Love Naturally?
Demons can be said to love in a natural way, but not in a supernatural way. First let us consider that demons do love in a natural way.
Spiritual beings, such as angels and demons, are possessed of an intellect and, more importantly, a will (ST Ia.59). The movement of the will is love:
Consequently, in the intellectual nature there is to be found a
natural inclination coming from the will; [...] Therefore, since an
angel is an intellectual nature, there must be a natural love in his
will. (ST Ia.60.1.c)
...but in so far as [love and joy] express a simple act of the will,
they are in the intellective part: in this sense to love is to wish
well to anyone. (ST Ia.59.4.ad2)
Now the only sins of the demons are pride and envy (ST Ia.63.2), but both of these sins presuppose love of oneself. Envy occurs when "another's good is apprehended as one's own evil" (ST II.II.36.1.c), and the shunning of one's evil presupposes the love of one's good. "Consequently love must needs precede hatred; and nothing is hated, save through being contrary to a suitable thing which is loved" (ST II.I.29.2.c). Pride is an excessive "love of one's own excellence" (ST II.II.162.1.obi2). Thus all demons, including Satan, must at least love themselves.
Aquinas may even imply that demons love God insofar as God is the source of their natural being, but fail to love God in a supernatural way due to their mortal sin. He says,
It is natural for the angel to turn to God by the movement of love,
according as God is the principle of his natural being. But for him to
turn to God as the object of supernatural beatitude, comes of infused
love, from which he could be turned away by sinning. (ST
This leads us to the sense in which demons do not love: by way of supernatural charity.
Do Demons Love Supernaturally?
Demons do not love supernaturally. Thomas makes an argument that demons are Cherubim and not Seraphim because the demons sinned mortally and mortal sin is incompatible with the fiery charity of the Seraphim:
Cherubim is interpreted "fulness of knowledge," while "Seraphim" means "those who are on fire," or "who set on fire." Consequently Cherubim is derived from knowledge; which is compatible with mortal sin; but Seraphim is derived from the heat of charity, which is incompatible with mortal sin. Therefore the first angel who sinned is called, not a Seraph, but a Cherub. (ST Ia.63.7.ad1)
Indeed, no creature in a state of mortal sin possesses the supernatural love of charity. Since the demons are in a state of mortal sin they do not possess this kind of love. Indeed, it could even be said that in committing the sin of pride Satan loved himself more than he loved God. Thomas quotes Augustine, "[Satan] wished to enjoy his own power rather than God's" (ST II.II.163.2.c).
Could Demons Love Supernaturally?
Thomas is clear that demons cannot change their minds and convert. "According to Catholic Faith, it must be held firmly both that the will of the good angels is confirmed in good, and that the will of the demons is obstinate in evil" (ST Ia.64.2.c). This is because the angelic intellect operates in such a way that once it has adhered to a thing, it does so immovably. So demons could have chosen to accept God's grace and enter into supernatural love, but having once decided to shun God, they can never go back again:
Therefore, if [the angel's] will be considered before its adhesion, it can freely adhere either to this or to its opposite (namely, in such things as he does not will naturally); but after he has once adhered, he clings immovably. So it is customary to say that man's free-will is flexible to the opposite both before and after choice; but the angel's free-will is flexible either opposite before the choice, but not after. (ST Ia.64.2.c)