Here are some moves it can learn and will learn: Sludge bomb, Leech seed, Razor leaf, Vine whip, Hyper beam, Earthquake, Frenzy plant, Solarbeam, Giga drain, Mega drain, Body slam, Toxic and many more such as Sleep powder, Poison powder, Stun spore.
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Venusaur learns solar beam at level 65 in Red, Green, Blue, Yellow, Gold, Silver, Crystal, Ruby, Sapphire, FireRed, LeafGreen, and Emerald. But Venusaur learns solar beam at level 53 in Diamond, Pearl, and Platinum.
The last move, in fire red, that Charizard learns is Fire Spin. That is at Level 55.
Venusaur learns Sleep Powder at level 15, but assuming you are using a legit, evolved Venusaur, you can do one of these two. 1. Train an Ivysaur to learn Sleep Powder at level 15 2. Have the move tutor teach it to your Venusaur (I don't think move tutors exist in Pokemon Red/Blue/Yellow)
Your rival will have a Venusaur if you chose Squirtle as your starter.