How do solar winds affect the atmospheric composition and density of planets? Here is a bit of a newbie question, if you please. 

The sun is constantly ejecting small particles via solar winds that come into contact with planets and other objects in our solar system. Do these particles contribute to the planets's atmospheres? Or do they do more harm than good? (define: good = contribute).

Do solar winds contain any larger atoms than helium. For instance, Oxygen? 

My intuition on this issue is mixed since we have Mars with a very thin atmosphere, but Venus with a very thick atmosphere, neither having a very strong magnetosphere to protect them from solar winds.
Do these particles contribute to the planets' atmospheres? Or do they
  do more harm than good? (define: good = contribute).


That depends on the size (mass/escape velocity) of the planet.   See atmospheric escape and pretty picture



For the 4 inner planets, the solar wind strips gas from the planets.  This process if fairly straight forward.   It has more to do with heat than traditional "blowing", and when the when the outer atmosphere gas molecules reach a certain temperature they can achieve escape velocity.   Earth mostly just loses hydrogen and helium and very little of it's heavier gases.   Venus over time has lost most of it's Methane and Water Vapor, the key difference between Earth and Venus is that Earth has a magnetic field.

Mars has lost most of it's atmosphere and what atmosphere Mars retains may be related to the thawing and re-freezing of it's icy poles, and Mercury's atmosphere is so thin that it's atmosphere actually is little more than a loosely retained collection of solar wind particles.

The 4 outer planets don't lose much to the solar wind and the Solar wind (I would think) adds to rather than takes away from their total mass, but this addition is very small compared to the mass of a planet. 


  Do solar winds contain any larger atoms than helium. For instance,
  Oxygen?


Yes, but only trace amounts.  The Solar wind is 92% hydrogen and 8% helium.  Source.  Very close to the universal average ratio.   Solar particles are so hot that when they're ejected from the sun the electrons and atomic nuclei are largely separated so you get a stream of charged particles, electrons and protons being the most common and Alpha Particles (Helium Nuclei) 3rd.  This means that any planets with a magnetic field, those particles get caught in planet's magnetic field.   That's why a magnetic field is considered very important in preserving a planet's atmosphere.

Some of the captured solar wind particles would probably get deposited into the Planet's atmosphere over time but I'm not clear on that process and I don't know the percentages.  

Getting back to the Sun, it has about 2% "heavy" elements in it, see article, and by "heavy" I mean, Oxygen, Carbon, Neon, others, but gravity draws the heavier elements towards the center of the sun.   Also, the helium the sun creates is largely formed near the center of the sun, so the outer parts where the solar wind gets ejected has a more standard/universal balance of about 92% hydrogen by element.


  My intuition on this issue is mixed since we have Mars with a very
  thin atmosphere, but Venus with a very thick atmosphere, neither
  having a very strong magnetosphere to protect them from solar winds


Venus mass is sufficient to make a difference.  Atmospheric escape has to do with escape velocity from the planets and Venus' escape velocity is over twice Mars'.   Source.  Venus' atmosphere is also sufficiently thick that it generates it's own magnetic protection of sorts, (I've read that, didn't see a good article to reference just now).   

Jupiter has an enormous magnetic field, which casts a pretty big net, much larger than the planet itself and that captures solar wind particles, but compared to the mass of Jupiter, the captured solar particles, even with the large magnetic net, is teeny-tiny and makes no real difference in the mass of the planet.

Interestingly, when the sun approaches it's red giant stage, it's ejections will significantly increase, so it's possible that, 5 billion or so years from now the sun will feed Jupiter a stream of particles in a measurable way and Jupiter will grow larger and perhaps, visibly glow due to the particles it receives.  Jupiter might be a fun planet to watch when our sun goes red giant, perhaps from the safe distance of a colony on Saturn's moon titan.   But that's just speculation.   :-)   

It will never turn into a star, it's far far far too light for that, but Jupiter could still be fun to watch (from a safe distance) 5 billion years from now.   (My answers always tend to be too long). . . 

Corrections  welcome.