What are the fields of eudaimonology and soteriology in philosophy? Here I will attempt an original overview of an answer. I happen to be very interested in each of them individually but in this short piece I hope to give some indication of how they are similar to, and how they interact with, one another.
If the eudaimonic tradition from ancient philosophy is focused upon the highest good or best way of life for humankind then eudaimonology is the study of those things that determine what that way of life is like. Indeed, this is the most familiar use of the term ‘philosophy’- what one’s way of life is focused on.
Soteriology has a more conventional definition: the study of salvation, that is, of making people safe or secure. This involves being absolutely free from stress, anxiety and guilt, and in theistic traditions, being loved and valued for who you are. As such it is the field that separates of theology from other branches of philosophy. I regard this as the necessary and sufficient condition for something being theological, because while ‘relying on the authority of a sacred text’ is often touted as a necessary condition, there are many scholars and texts that recognisably do theology without doing this.
The most important substantial (rather than formal) difference between ethics in the eudaimonic tradition and in the analytic tradition is that the former sees morality as intrinsically bound-up with the meaning of life and happiness.  This is a ‘thick’ concept of ethics, in contrast with the thin concept whereby it deals solely with what acts we should or shouldn’t do and why. This kind of joined-up thinking will be more difficult but it will also be more comprehensive and useful to society.  Indeed, another characteristic of eudaimonic thought is emphasis upon civic duty and participation in politics. This encourages us to see political philosophy as part of ethics rather than a separate field.
Eudaimonology looks at morality, meaning, and happiness together to elucidate them through discovering their proper relation, with a view to improving people’s lives. Here we have a significant formal difference with analytic philosophers, that the eudaimonist is a sage who is actively seeking to spread her insights about human life to benefit others. Soteriology shares this prescriptive attitude, and rightly so: if you have reason to believe that you can teach people things to improve themselves that is reason enough to do so. I don’t mean to suggest that most analytic ethicists aren’t concerned citizens and moral people, but rather that they don’t believe that their knowledge of the subject translates into an expertise for helping others. 
I think that this is most unfortunate. It is true that philosophers cannot be reliably taken to be more moral than other people, and that morality is not something theoretical but something practical, but moral knowledge is real knowledge and it is knowledge that philosophers tend to have a lot more of than other people. This tendency in philosophy is likely a lingering effect of the now discredited fact-value dichotomy. 
Some parallels can be made with soteriology. Like eudaimonology it deals with human life and human value at a very general level. As this makes for a more holistic picture, soteriology too deals with more than one kind of question. In the thin sense of the term, soteriology is just the study of how one can attain salvation, what one can do to be ‘saved’. But in a thicker sense it is also the study of what the nature of salvation is, why we might need to be saved, and by extension the nature of ultimate reality and mankind’s relation to it. As such it seems that soteriology includes eudaimonology within it, but expands into further spiritual and metaphysical exploration.
But lest the two fields merge into one homogeneous blob, I’ll bring out the main difference I can think of: while eudaimonology puts a very strong emphasis upon temporality, soteriology is inclined towards the atemporal. The emphasis upon temporality in the eudaimonic tradition takes the form of analysing morality, happiness and meaningfulness as phenomena that take long periods of time to come to fruition, requiring experience, training, and learning from mistakes. So the types of value and well-being eudaimonology studies are down to Earth ones that humans experience in their day to day lives, and which are the subject of change. I mean things like respect, duty, fidelity, and friendship.
Whereas the types of value and well-being that are involved in soteriology are more abstract and are directed atemporally, for example, a cosmic sense of justice or love. One does not (or at least should not) aim to be ‘saved’ in one particular moment and then the next. One aims to undergo a radical transformation of self-transcendence which unlike one’s moral standing does not depend upon when and where someone is in their life journey, which is not affected by the changing course of one’s life, and which makes sense as one is connected to something much larger and greater than the time and space we inhabit. The deep spiritual experience of safety, bliss, peace, or love that one can have a in a moment is importantly disconnected from that moment and directed towards something wholly other.
Soteriology is intertwined with eudaimonic thought because of the rich religious heritage of philosophical thought. Those with a broadly traditional view of philosophy are therefore naturally drawn towards soteriological issues from eudaimonic ones. I conclude that while soteriology contains eudaimonology within it, eudaimonology also naturally leads into soteriology. Thus there is no absolute distinction between the two.
1) Where classical utilitarianism defined goodness in terms of happiness this was a contingent identity claim. It is an example of ethicists choosing to talk about happiness, but my point is that it is a choice rather than a necessity; within analytic ethics it is entirely reasonable and acceptable for morality to be discussed in isolation from happiness. Obvious examples of this are Kantianism and Intuitionism.
2) In linking views on various issues together, rather than treating them as specialisms eudaimonology resembles the academic discipline called Human Sciences.
3) In recent years there have been quite a few analytic philosophers who have done eudaimonistic work, the names that spring to mind are: Philipa Foot, Mary Midgley, Alasdair MacIntyre, Charles Taylor, Michael Sandel and John Cottingham. But these are, as it were, exceptions that prove the rule. These writers have in the main been quite reluctant to use their field to call the masses to a better way of life.
4) Of course facts and values are different things, but they are not mutually exclusive as it was standard to hold for most of the history of analytic philosophy. For example, that ‘Hitler was a bad man’ is a value proposition doesn’t stop it from being an objectively true proposition, that is, a fact.