How are themes of exile used by Virgil in the Georgics and the Eclogues (1 and 9)? How does he elicit emotional responses (such as empathy) from the reader? How does nostalgia factor into these themes?
To begin, I would say that the theme of exile is prominent in the Eclogues (and especially 1 and 9) and a LOT less prominent in the Georgics as a whole. However, yes, in both you can see exile, empathy imparted to the reader, and nostalgia. And to show the optimism of all involved, let's take a famous quote from the Eclogues to prove happiness, even in exile:
Let us go singing as far as we go: the road will be less tedious.
In what is considered Virgil's most realistic Eclogue, we are immediately presented with the concept of nostalgia and empathy in regard to the feelings of the Italian residents after Julius Caesar's untimely death. At this time, much of northern Italy was taken away from landowners in order to give to soldiers. The landowners, then, were put into exile. We are presented with the story of Maliboeus who has been exiled as a result of this dispossession. Leaving baby goats as he tries to find a new home, he weeps about the lavish, cultivated land he is leaving. The reader has even more empathy for Maliboeus when when we find that Titryus has escaped exile by pleading in Rome earlier in his youth.
The ninth Eclogue echos the first (spoken of above). Similar to Maliboeus, this time it is Moeris who explains that, despite his efforts to keep his land due to writing poetry, he has been kicked off his lands by a new owner. Again, we find that soldiers are the new owners. Poetry, unfortunately, does not sway the soldiers' appetite for land and cattle. Again we see the nostalgia for the time of Caesar when Moeris talks about the new constellation and the star of Olympian Caesar. In the fray, Moeris escapes into exile (but only barely) and there's an homage to later English pastoral poets when Moeris rests by a river at the end of the Eclogue while watching the pruning of vines.
If you are going to go apart from the Aeneid, it is in the Georgics that it is hardest to find the theme of exile, but perhaps easiest to see the themes of nostalgia and empathy. This set is incredibly pastoral, so the beauties of country life and farming are stressed above all other occupations (at the grand request of Virgil's patron, of course). Nostalgia for country life by those who live in the city is paramount and, in fact, there is quite a lot of the Georgics that is actually a "how to" in regard to farming and crop cultivation. However, Seneca explains that
Virgil aimed, not to teach the farmer, but to please the reader.
We have empathy for the farmers as they struggle with rough soil and other things out of their control, such as drought and hail storms.
Exile, however, is harder to find, but I would point you to the last half of the 4th Georgic that deals with bees. In a sense, bees had been "exiled" from humankind and their usage of their honey since the death of Orpheus and Eurydice. Why? Because the sea nymphs are mourning their deaths. Aristaeus, who is upset at the death of his bees, finds out from Proteus the reason and sacrifices four bulls. From the carcasses of these bulls, a new swarm of bees bursts forth. This also is a "how to" in regard to the cultivation of a new swarm of bees. So, I'm afraid exile (in the Georgics) is limited to bees. HOWEVER, I suppose you could say that this pastoral, country life is also reminiscent of the exile of the Eclogues, for THESE are the ways that the exiled farmers are lamenting as they leave their lands to the soldiers.