What are some common themes and poetic techniques in the poems "Preludes" and "Rhapsody on a Windy Night"?    

T. S. Eliot was a modernist poet who often employed the technique of "stream-of-consciousness" writing in his poetry.  To explain, modernist writers tended to be disillusioned and upset with the world, focused on the industrial nature of life (meaning, city life) and how dreary and unfulfilling that was, and on people and characters who have difficulty connecting with each other or feeling like they belong.  They also liked to experiment with the form of their writing--so, their stories didn't follow chronological order, didn't have happy endings, and toyed with alternative styles of writing like stream-of-consciousness.  Stream-of-consciousness writing is very random; it's like you are just writing down whatever comes into your head, no matter if it fits or makes sense.  If often revolves around a theme, like the city streets at night, but then jumps around quite a bit, just like our brains do when we think.  You can see this style in Eliot's poems, because he lists a bunch of images, memories, and emotions, all thrown together in seeming discorded chaos.  It's just like he opened his brain and poured the contents onto the paper.  So, there are some thoughts about his style and technique.

He uses many poetic techniques.  Imagery is one of them--using the 5 senses to capture an emotion or scene.  Take a look at these lines from "Preludes III":

"Sitting along the bed's edge, where
You curled the papers from your hair,
Or clasped the yellow soles of feet
In the palms of both soiled hands."

Here, he uses imagery to convey the weary, run-down sight of this woman preparing for the day. Or, from section II,

"The morning comes to consciousness
Of faint stale smells of beer
From the sawdust-trampled street
With all its muddy feet that press."

Here he describes the smells, sights and textures of the city streets.  Look in his poems for any descriptions using the 5 senses, and that is imagery.  He also uses personification quite a bit, where he gives inanimate objects and ideas human-like traits.  For example, from "Rhapsody on a Windy Night," he states, "The memory throws up high and dry."  Memories cannot throw; that is giving memories human-like traits.  In Preludes, there is the "winter evening settles," the shower "wraps" and "beats,".  He also uses similes (comparing something using like or as)--

"The worlds revolve like ancient women/Gathering fuel in vacant lots."

For lack of space, I'll stop there, but I hope that those thoughts get you started on techniques and style.  For themes, he has the theme of run-down, depressing life in the city, of the meaningless life of city existence and trying to find meaning there, and how hard that is.  Themes of how real, fulfilled life that has beautiful sights and smells is always lingering, taunting on the edges, just out of reach.  How he feels life should be much more, but isn't.  Good luck!