And also, is the Jaya version available online in English?
It is said that Mahabharata, as it was originally written, was much shorter than its current form and was written under the title "Jaya". It is undisputed that the full length of the Mahabharata has accreted over a long period. The Mahabharata itself (1.1.61) distinguishes a core portion of 24,000 verses, the Bharata proper, as opposed to additional "secondary" material, while the Ashvalayana Grhyasutra (3.4.4) makes a similar distinction. According to the Adiparva of the Mahabharata (shlokas 81, 101-102), the text was originally 8,800 verses when it was composed by Krishna Dwaipayana Vyasa and was known as the Jaya ("Victory"), which later became 24,000 verses in the Bharata recited by Vaisampayana, and finally over 90,000 verses in the Mahabharata recited by Ugrasravas.
Below is an excerpt from Wikipedia:
At least three redactions of the text are commonly recognized: Jaya (Victory) with 8,800 verses attributed to Vyāsa, Bhārata with 24,000 verses as recited by Vaiśampāyana, and finally the Mahābhārata as recited by Ugraśrava Sauti with over 100,000 verses. However, some scholars, such as John Brockington, argue that Jaya and Bharata refer to the same text, and ascribe the theory of Jaya with 8,800 verses to a misreading of a verse in Ādiparvan (1.1.81). The redaction of this large body of text was carried out after formal principles, emphasizing the numbers 18 and 12. The addition of the latest parts may be dated by the absence of the Anuśāsana-parva and the Virāta parva from the "Spitzer manuscript". The oldest surviving Sanskrit text dates to the Kushan Period (200 CE).
This fact of Jaya as the original version of Mahabharata became popular when the popular Indian writer Devadutta Pattanaik wrote a book "Jaya: An Illustrated Retelling of the Mahabharata". However, this book is just a fictional version of the current Mahabharata that recounts various stories from folklore and regional versions of Mahabharata. Hence it must be clarified that Pattanaik's Jaya is not the actual version mentioned in the scripture.
The essential difference between Jaya and Mahabharata is summed up here:
Jaya was about spiritual victory, Vijaya was about material victory, Bharata was the story of a clan and Mahabharata included also the wisdom of the land called Bharat-varsha. What began as an auspicious idea, ended up becoming a massive documentation of realities that frightened the common man.
The original Jaya is not known to us, since that book itself underwent multiple expansions and is now known to us as Mahabharata. Before the tradition of writing down scriptures began, just like Vedas even Mahabharata was orally transmitted.
However, vedas are made error-proof by memorizing and chanting the hymns in various combinatorial ways or patha (eg: ghana patha or danda patha). These pathas are painstakingly repeated in a particular sequence (eg: 1-2-2-1-1-2-3-3-2-1 for ghana) where each pada has its unique pattern of svara (pitch). So even a slightest change to the pada, matra or svara in that mantra will disturb the whole of the combinatorial patha. In this way vedas are made fool-proof to careless modifications creeping in due to time.
But unlike vedas, a smriti like Mahabharata is only chanda bound (has specific metre). Hence you can change the internal wordings of the poetry, or even add more verses to it as long as the metre is not disturbed. Hence until the time it was written down Mahabharata was vulnerable to editing by scholars to make its context and meaning seem suitable for their time and culture. In this process the original Jaya might have been lost, and the current version sustained due to written documentation.