On the basics of political opinion - Are you sure you mean what you say?

This is an attempt to clear the air over political opinion, as they say, left right and centre. And it does coincidentally have a lot to do with the left and the right and what they mean in today's world.
Being either left or right, depends on which context you're talking about.
A. From an economic viewpoint
B. From a social viewpoint
While A is more well known, a definition that does not include B will be inadequate.

Being left in the first context means a close protected economy that provides adequate protection for local industry, workers, encourages government intervention in the market. For instance, Nehru's idea of having state-run industries that provide job security and the communist parties, today with their opposition to foreign investment in any sector are also left in the economic sense.

Being right would mean being supportive of an open economy, allowing foreign firms to compete with local industry, encouraging foreign investment, and more flexible labour laws that allow firms to operate competitively at the cost of hiring and firing people freely. Being right thus, means being economically liberal.

These however, are the usual context in which left and right are discussed. However, people don't vote on an economic basis alone.

For instance, they hardly knew a thing about economics, when the people of Gujarat voted back to power, the BJP after the riots. More so, the economy was going from bad to worse. Bush's decision to veto any funding for a specfic stem cell research program has the support of a large number of people, not because it's economically unviable, but because their social viewpoint concurs with his.

Differences in social opinion have largely to do with religion, tradition and customs. People inclined to their religion and tradition are generally referred to as conservative. So clearly orthodox brahmins, devout muslims, christians and jews all fall in this category, so do homophobic people,who usually are one of the former. For instance, conservative people might want to prefer sexual abstinence and sex with a single married partner as a solution to an AIDs problem.
All parties with a religious inclination, and a caste affiliation are by definition, conservative.
India, by this definition is largely conservative, with roles for men, women defined as per what is considered tradition, customs followed rigorously, be it religious ceremony or dowry during marriage. As is reflected in the general inclination of most young men and women to marry within their community and the high degree of homophobia prevalent. (Being homosexual is illegal in India)

On the other hand, people who do not take either religion or tradition seriously would be called liberal. People who don't really care about either, and perhaps look at them as being forcefull imposed on them, like young people in most western countries. Liberals would be willing to break what is generally perceived to be tradition, not be homophobic. So, to compare them to the conservatives above, liberals would encourage sex education, promote safe sex between partners, advise gay partners on the high risk nature of their sexual relationships than denounce them as immoral.
Liberals would thus, be more willing and likely to marry people, not necessarily liberal(simply because they don't care), from different ethnicities, religions and castes.

Something that would strike the more-than-casual observer is how the two divisions are combined, for it is always right-conservative and left-liberal, right-liberal is not very common and being left-conservative can sound hypocritical.
For if you belong to the economic-left, you merely signal that you are in favour of a uniform system that grants a minimum to everyone, regardless of their ability, a system that takes care of the poor and the not-gifted.
By the same measure, left politicians cannot be in favour of a system that grants more favours to one particular affiliation(religion or group or sexual inclination) and hence, are likely to be more tolerant, and would be classified more as liberal than anything else.

So the Congress(I) in the given circumstances in India is liberal. Also, the policies of P Chidambaram, would be more right, than left, if not for the coaliton with the left. In which case, we have a right-liberal, ie liberal on both fronts - social and economic.

Given these basic definitions and a understanding that parties cannot always be put into one of these four divisions - as they turn to be not water-tight in an Indian context, I would associate the following major Indian parties with these inclinations.
I consider caste as a criterion for being conservative/not only if the party is clearly partisan like the BJP, BSP - for Dalits and not just on the basis of the caste/religious identity of the leader.For instance, it is well known that in Andhra Pradesh, Kammas have a bigger influence in the TDP, while the Reddys do so in the state Congress - however,their policies are not in favour of these communities unlike the BJP or the BSP.
Also, given the nature of Indian politics, most parties are largely populist, hence left, with brief streaks of economic liberalization when things went out of control.

1. Congress - Left-Liberal (Manmohan's liberalisation programme, meant right-liberal in 1991)

2. BJP - Left-Conservative( Given, the senior leaders' partisan view that favours the Hindus)

3. TDP - Left-Liberal (right liberal in the late 1990s, when Naidu was the darling of the west, including being named Time Asia Person of the year 1999)

4. DMK - Left-Conservative (Given their partisan nature that favours Dalits but not Brahmins)

5. BSP - Left-Conservative (Highly partisan - Dalits)