In 1984, what are some internal and external conflicts?

Most of the internal conflicts arise from Winston's
unhappiness with his life, and his suspicions that it is the Party that is the cause. 
At the beginning of the novel he is absolutely miserable, and that misery is mostly
caused because he hates the Party and feels like he is the only one. He cannot be happy
with it--it is an interna, Man vs. Self issue (even though his unhappiness is caused by
the Party, Winston is conflicted with his angst about it).  He struggles each day to
even have motivation to get up in the mornings.  He wishes so badly to know more--more
people who feel the same, more about the history of the Party, and more about what
causes true happiness.

So, internal conflict comes from
Winston himself.  After he meets Julia, he is conflicted constantly about his paranoia
of being caught.  It is always there, like a haze over his happiness.  He is also
internally conflicted about whether or not to make himself known to O'Brien; his fear of
being caught battles with his desire to be part of a larger group of
rebels.

The external conflict comes from the fear and
repression that the party puts on its members.  They are constantly watched by Big
Brother, which leaves them living in continual fear of punishment for rebellion.  They
are even afraid to sleep, as their subconscious minds have betrayed them as they were
sleeping.  The party maintains that external fear through contstant examples of
punishment, encouraging others to turn neighbors in, and
propaganda.

Other external conflicts come at the end with
Winston's torture and the slow deterioration of his body, and accordingly, his mind. 
The torture techniques appplied are external conflicts, that stem off of his internal
fears of losing his mind, losing his love for Julia, and giving in to his worst
fears.

I hope that those thoughts help to get you started;
good luck!