Humble Food Offered to Rama and Krishna and accepted with great respect

Jhoothe phal Sabari ke khaaye, Saag Vidur ghar khaayee
Shabari (Berry) - Vidur patni (Banana + Sarson da saag) -

Incarnation of Jay Vijay / Story

Ravan - Kumbakaran
Shishupal - Dantavakra
http://www.suite101.com/article.cfm/mythology_from_india/90641/1

Gurus of Rama / Krishna

Vashishth + Vishwaamitra - 

https://freeglobaluniversity.blogspot.com/search/label/Vz

Gargaachaarya + Sandipani

https://harekrishnainfo.blogspot.com/search/label/KrishnaBalaramaGuru

Impact of Ramayan on Mahabharat

Main important events of the two epics are almost similar. Let's see them first.

1. King Dasharath was cursed by a sage, as he mistakenly pierced the sage's son, & that curse was responsible for his tragic death. Similarly, King Pandu was also cursed. He too made same mistake, as he didn't recognize the sage who was disguised as a deer. Pandu too, died of that curse!
2. The swambar of Draupadi was based on the test of Astra-Vidya, which is similar to the case of Sita. Both Drupad & Janak wanted the real hero as their sons-in-law, & arranged swambar. Only the breaking of Haradhanu is replaced by the piercing of fish.
3. In both epics, the elder prince had to sacrifice his kingdom & all royal belongings, & both were banished with wife & brother. I know that the background of the Van-gaman of Dharmaraj is not similar to that of Ramchandra, but it may be thaught that the idea of banishing an innocent prince unfairly is the direct effect of Ramayan. Vyasdev has modified the fact & changed the background to keep pace with his society, but couldn't avoid the effect of Valmiki.  
4. In both epics, heroin welcomed vanavas with her husband, & was abducted. Draupadi was abducted by Jaydrath, but Jaydrath was punished at once by Bheem & Arjun. Besides, Sita had to suffer painful insult from Ravan, similarly Draupadi was also insulted by Duhsashan & Duryodhan.
5. In both epics, the hero burst into anger after his wife was insulted severely, & became ready to take revenge. In both epics, the causes of war are very close. Ram started war to make Sita released from Ravan's hands, while Pancha-Pandav started war to get back their kingdom! "Patni-uddhar" in Ramayan & "Rajya-uddhar" in Mahabharat, are the main causes of war.
6. Both of the heroes became the winner, & both were Dharmayuddha. After both of the wars, Dharma was well established in earth.
7. In both the cases, the desire of the hero was fulfilled, but none could enjoy them! Neither Ram nor Yudhisthir could spend a completely peaceful & happy life even after the war! In both epics, when all of the external problems were finished, the internal problems came into play & threw the heroes into the ocean of unbearable grief. Ram had to banish Sita in order to serve the Raj-Dharma, & Pandavas lost their mental peace, in Shanti Parba, Dharmaraj broke down completely & wanted to leave the kingdom. It can be noted that they didn't face any mentionable happy moment after the war was finished! Rather they had to watch destroy of Yaduvangsa like a dumb spectator; they lost their relatives, & the best friend Krishna. All of those incidents were responsible for the decision of Mahaprasthan.
8. Both the epics have a tragic end. All the main characters died at last. But it's noticeable that, Ram had to sacrifice Sita & Lakshman first, & then he decided to leave the earth. Similarly, Yudhisthir also had to sacrifice his four brothers & Draupadi, & then he went to heaven!