Moon can occult Venus. Venus can transit across the solar disc. Moon can elipse Sun. Can all three celestial events occur at the same time - Moon is at front of Sun (partial eclipse is fine) and Venus is behind Moon (ideally part of the planets is seen at lunar limb)? Observer is at Earth.
Yes, but such an event would be very rare. Venusian transits last only about 7 hours, and there are only two in 113 years, So Venus is in transit for about 0.0015% of the time.
So as a back-of-the-envelope calculation, you would need to see about 70000 eclipses before you had a combined transit/eclipse. There are about 2 solar eclipses a year, so you might hope to get this unusual syzygy once every 35000 years or so.
None are forecast.
Some of your description, and the answers to date, assume that Venus has to transit the Sun. That is not a requirement for the literal question "can lunar occultation of Venus occur during a solar eclipse". Likewise, the description says "three" events but only gives two conditions: Moon is at front of Sun and Venus is behind Moon.
If you remove the restriction of a Venus transit, then an occultation of Venus can occur during a solar eclipse when Venus is up to half a degree away from the Sun. The Moon is about half a degree across, so the Moon can be occulting Venus and creating a partial solar eclipse at the same time. At half a degree Venus-Sun separation, the event begins and ends simultaneously. If the Venus-Sun separation is less than half a degree, the duration lasts longer. (A total occultation can last up to approximately 1 hour, so that would be the maximum duration.)
Also, if the restriction of a Venus transit is removed, Venus can be at superior conjunction (on the far side of the Sun) and fulfill the requirements of an occultation during a solid eclipse.
Of course, seeing Venus when so close to the Sun but not transiting the Sun would be very challenging (and dangerous!). From the perspective of actually seeing the event, I agree that a Venus transit is virtually a requirement.
The simultaneous occurrence of a solar eclipse and a transit of Venus is currently possible, but very rare. The next solar eclipse occurring during a transit of Venus will be on 5 April 15,232. The last time a solar eclipse occurred during a transit of Venus was on 1 November 15,607 BC.