Contradiction in Ohm's Law and relation $P=VI$

There is no contradiction here. In fact, the power equation is often represented in different ways:

\begin{eqnarray}P & = & IV\\ P & = & I^2R \\ P & = & V^2/R \end{eqnarray}

The equations can be manipulated depending on which variables you are controlling.

Most commonly, your circuit has a particular resistance. Your power source has a particular voltage. And so you can figure out the current, by working out $I=V/R$. Bigger voltage is bigger current. Bigger resistance is smaller current. In this same situation, you can work out the power that's going into the circuit. You know all three, so the power will be the same whichever equation you use. But, since you know the voltage and the resistance, you might say that $P=V^2/R$. So doubling the voltage will quadruple the power.

To be specific, $V$,$I$, and $R$ are going to be related by Ohms law for a given circuit. If you adjust one, one of the others will change. The power law can then be used to figure out how much power is being used in the circuit.

When you are going from an equation to a proportionality statement you need to be mindful of what is being kept constant.

$V=IR$ means that $I$ varies directly with $V$ if $R$ is constant.

$P=IV$ means that $I$ varies inversely with $V$ if $P$ is constant.

The only time you could get a contradiction is if you are comparing situations where the power is constant and also the resistance is constant. But if that's the case you'll find there is only one solution for $I$ and $V$, that is to say, with those restrictions $I$ and $V$ can't vary - directly or inversely.