Let's 1st understand what these planets represent on their own?

Sun - Sun represents Soul, Personality, King, Government, Father, Authority, Career, Top Positions, Ego, Self Esteem, Health, Education etc.

Venus - Venus is Beauty, Desire and Love, Liquid Money. Venus is the main significator of marriage. Venus represents girlfriend or wife for a man. Venus is the significator of all relations, may it be husband-wife or mother-daughter. Philosophically speaking, Venus is also the cause of all the sufferings in our life. How? Because Venus represents our desires and we get pain and suffering in our life only when our desires are not fulfilled.

Rahu - It represents Illusion, Foreign Lands, Foreign Things (foreign as in unknown things. So, for someone living in Punjab, culture and rituals of Kerala is also unknown and hence Foreign), Drugs, Medicines, any type of intoxication, Fame, Wealth, Success, Obsession, Past-life incomplete Desires, Movies, Television, Online World, Cheating, Imagined Fears, Unusual Things, Unique Things, Creativity, Rule breaker. Rahu also blows things out of proportions. 

3 planetary conjunction - Whenever 3 or more planets are conjunct with each other in a house/sign then things related to that house/sign become a kind of life focus for person. It is because of huge accumulation of energy within 30 degrees of sky. It means not only these 3 planets' energy is going into this house/sign but the energy of at least 4 to 6 house/sign is going into this house/sign as these planets will be ruling some houses too. So, this house/sign with conjunction becomes almost the most important house in chart. During Career Consultation, I give a huge importance to any such house which has 3 or more planets in it.

House Ruler - Besides these karaka things, Sun, Venus & Rahu will also rule some houses in your chart and will represent things related to that house. Of course we can't cover conjunctions Ascendant and house wise else it will never be over. So, you have to include things related to the houses at the time of interpreting this conjunction. Also, we need to keep in mind all Yogas and Raj-Yogas which their conjunction would be making to completely understand the conjunction. Here, we can only cover meaning as per karakas.

Meaning of Sun-Venus-Rahu Conjunction - As I said, because Venus is with two malefics Sun & Rahu, it hurts the relationship aspect in life. This person can have real illusion around relationship. They can jump into relationship from nowhere and later may regret. Rahu with Venus can give some of the most illusive love stories specially in Venus-Rahu or Rahu-Venus dasha. Again, person is born near solar eclipse so they may have a problem related with finding their right career or right path in life. It can be a distant relationship with father depending on how close someone is born to solar eclipse. If Venus is in between Sun & Rahu, it can reduce the results of relationship due to paap kartari yoga but it can bring a foreign spouse in life. Person may love to live on showing off his ego and authority. They can have real troubles with authority. On positive side, Rahu can enhance person's wealth and creativity without any limit. They can be filthy rich or like to be one. They can be fond of super-rich or celebrity-like life style. Ego conflicts can be a reason behind loss in relationship here. 

Who will win the Conjunction? - As Rahu is impacting Sun & Venus both, Rahu is winning the conjunction. 

Dignity & Strength - 

In any sign/houses, results will be similar for Jeeva Karaka at least.