1. Non-violence in Vedic tradition being independent of Buddhism / Jainism should not be surprising because expressions of non-violence or expressions such as "Ye, don't commit violence against...." are part of mantras of Rigveda and Yajurveda themselves. There are several mantras ending in मा हिंसीः।  

2. But the characteristic of Vedic tradition which baffles a non-discerning observer is the thriving of its ideal of non-violence  always alongside its allowance to harm, kill, punish etc. There are Vedic mantras instructing to harm/kill harmful entities. Some mantras express a wish for courage, strength to succeed in such harming/ killing / punishing. 

That one way of looking at 'non-violence' is to save entities vulnerable to violence from such violence by resorting to violence against those committing violence against such vulnerable creatures is a subtle understanding of non-violence inherent in the Vedic world-view. क्षत्त्र or क्षत्त्रिय is an agent of such non-violence (no violence against the weak / vulnerable).

3. It is this subtle understanding of violence and /or non-violence rooted in the Vedic tradition right from the Veda mantras that is inherent in Mahabharata that fails a superficial reader of it in understanding the congruence of अहिंसा परमो धर्मः with the remaining parts of the book that make the book appear to be a book of war. 

4. Let us take the portions of the book that can not but be integral to the book and see if they have vegetarianism and non-violence. 

One such portion is  संभवपर्व , शकुंतलोपाख्यानम् । It can not but be integral to the book because it provides the source of the name of the book itself. It is the story of the birth of the वंशकर्ता of the वंश after which the book is named. The book or at least its early chapter is a वंशचरित्र and is structured as such. Within that वंशचरित्र , this portion is the most vital one because it is the story of the birth of the वंशकर्ता of the वंश after which the book is named. 

Now, in that story, one of the most significant characters is कण्व महर्षि। 

कण्व is described in that narrative as a vegetarian, non-violent sage. 

His non-violence is indicated through the description:

तत्र व्यालमृगान्सौम्यान्पश्यन्प्रीतिमवाप सः ||१८||

He (Dushyanta) was pleased to see even wild animals being mild (gentle) there (in Kanva's ashram)

Entire ashram is described in detail. Not even a single violent activity is described. Shaastras studied there are described.

in detail. None of them is a shaastra related to wars or such violent activities.

When asked about Kanva, Shakuntala says,

गतः पिता मे भगवान्फलान्याहर्तुमाश्रमात् | मुहूर्तं सम्प्रतीक्षस्व द्रक्ष्यस्येनमिहागतम् ||९||

Bharata growing on that campus, is described as

सिंहसंहननो युवा |

षड्वर्ष एव बालः स कण्वाश्रमपदं प्रति | व्याघ्रान्सिंहान्वराहांश्च गजांश्च महिषांस्तथा ||५|| बद्ध्वा वृक्षेषु बलवानाश्रमस्य समन्ततः | आरोहन्दमयंश्चैव क्रीडंश्च परिधावति ||६||

This violence by Bharata is not condemned by the extremely non-violent sages there.

Moreover they praised him for the valour and gave the title Sarvadamana to him.

ततोऽस्य नाम चक्रुस्ते कण्वाश्रमनिवासिनः | अस्त्वयं सर्वदमनः सर्वं हि दमयत्ययम् ||७||

Why did Dushyanta go there? For the violent activity of hunting.

But he showed extreme respect towards the extremely non-violent sages lead by Kanva.

Non-violent sages encouraged violent Bharata and violent Dushyanta showed utmost respect for the non-violent sages.

(to be continued)

Why non-violent sages encouraged violent Bharata?

Since क्षत्त्र or क्षत्त्रिय as an agent of such non-violence (no violence against the weak / vulnerable), needs valour. 

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One of the most prominent faces of movements of non-violent movements and environmentalist movements today is the anti-war philosophy.

Is Mahabharata an anti-war book? 

What is the angirasa of Mahabharata according to Anandavardhana? 

śānta.

What is the sthāyībhāva of śānta?

nirvēda or śama. 

What does that mean?

Aanandavardhanaachaarya of 9th century AD read the book as the one with vairāgya as the central emotion, not as a book of war and violence. 

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Is there an internal evidence in the book for the view that the book is an anti-war book?

What is the udyōga (effort) in udyōgaparva? 

The parva has simultaneous efforts of preparation for war and prevention of war. 

Let us take bhagavadyānaparva portion of udyōgaparva. 

There is a huge anti-war portion of  the lecture by Yudhiṣṭhira here. 

युद्धे कृष्ण कलिर्नित्यं प्राणाः सीदन्ति संयुगे |

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जयो वैरं प्रसृजति दुःखमास्ते पराजितः |

सुखं प्रशान्तः स्वपिति हित्वा जयपराजयौ ||५९||

जातवैरश्च पुरुषो दुःखं स्वपिति नित्यदा | अनिर्वृतेन मनसा ससर्प इव वेश्मनि ||६०||

and so on.

Does this mean that the entire discussion is anti-war? There is a long debate back and forth for and against war in this episode. Among many arguments offered in justification of war, the one that repeatedly crops up is the justifiability of punishment to the offenders of Draupadi. 

Then what is the whole context of the anti-war talk ?

The line of argument in all the lectures including that of Sri Krishna is that to prevent war is the foremost priority as per Dharma. But to allow the villains to grab the portion of kingdom even after the condition of vanavāsa and ajñātavāsa is fulfilled is also not Dharma. After all the Dharmas are balanced, the net result is that war should be executed only as the last resort only after exhausting all the options available for preventing the war .

This priority for prevention of war is what is being highlighted here as part of the discussion on non-violence.