If these don't go much further back than the modern era, what did English speakers use before our time?
The Hebrew Bible, the Greek New Testament, and the Latin Vulgate translations of both all have interjections, so it's safe to say our medieval monk or nun translator would have been familiar with them no matter what. Most of them are some form of "a" or "ha" as a cry of woe (think German "ach", which is itself medieval).
And we see them in medieval English Bible translations. For example, the "a a" of the Vulgate's Joel 1:15 remains "A a" in the 14th century Wycliffe Middle English translation:
Alas for the day! For the Day of the Lord is here
A! A! to the dai; for the dai of the Lord is niy
I'm not as familiar with the Old English Bible and which books of it survive. The Gospels do, for sure, and the Wessex Bible gives "Ƿala!" as the exclamation in the middle of Mark 15:29:
Those who passed by derided him, shaking their heads and saying, “Aha! You who would destroy the temple and build it in three days, ave yourself, and come down from the cross!
And ða ðe forþstopon hine ȝremedon, and hyra heafod cƿehton, and ðus cƿædon, Ƿala! se toƿyrpþ ðæt tempel and on þrim daȝum eft ȝetimbraþ
Interjections have plenty of fun in English poets like Chaucer and especially in drama (not a surprise). "Ha" (or just "a") is already the written form of a laughter sound at least by the late Middle Ages.
I'm a Germanist, though, and I want to share one of my favorite observations about language. The monastic authors I study are mostly women, who know Latin for liturgical and biblical purposes, and often very well, but are generally more comfortable in their vernacular (Middle High German, mostly). In their writing--sermons and mystical poetry, for example--they often use vernacular interjections in the midst of Latin. Hildegard of Bingen (12th century) throws "Wah auf!" (wake up!) into the middle of an apocalyptic sermon she preaches to a public audience. Ursula Haider (15th century) cries out "Weh! Weh!" to God ("woe" or "ouch"; Latin vai is similar). I love moments like this because it can be so hard to get from written text to spoken--and language switches for outbursts like this seem organic enough to reflect something more likely spoken in fact than carefully crafted in editing.
And as with English, they're definitely not all negative in German. Hans Folz in the late 15th century uses "ja je je ja" as laughter and as meaningless babble.
I have a related question that I don't want to start my own thread for! What about swear words used in similar contexts? E.g. I stub my toe and say "ah, fuck" while I try not to cry, or something bad happens and I say "well, shit". Is there anything of the sort recorded going back a few centuries?