Chris Tilling puts it well, I think: our understanding of what Scripture means is very much influenced by our understanding of what the gospel is.
If, for example, we think that the gospel is primarily about how individuals get saved from their sin, enter into a personal relationship with Jesus and go to heaven when they die, then this becomes the lens through which everything else is seen. So,
If I read ‘righteousness of God’ it must point to something I get in order to cancel my sin and be saved (I’m deliberately being course [sic] with this description).
If I read Jesus’ words: ‘Truly I tell you, it will be hard for a rich person to enter the kingdom of heaven’ (Matt 19:23), this must mean that I need to be careful with my wealth or I won’t go to heaven.
If I read of the power of sin in Paul, or seeking to be justified by law, all must revolve around my sin and my legalism etc.
But although such readings may not be actually ‘wrong’, they do distort the meaning of the texts themselves, because coloured by a story which is not quite scriptural itself. Thus,
This is a complex one, but in my view the righteousness of God is not simply something that makes up for the hole in me after my sin is forgiven (or something like that). It is God being faithful to his covenant promises to defeat evil and renew creation, a movement up into which individuals are caught. But to see this one will have to read the scriptures with different ‘lenses’ – one informed more thoroughly by the scriptural narrative.
To enter the kingdom of heaven is not to enter heaven. They are not synonymous. ‘Heaven’ was just a pious way of avoiding saying ‘God’, and Jesus here is speaking of entering the kingdom of God, i.e. the economy of existence over which God is undisputed King. This may be related to some notions of ‘going to heaven’, but they are not synonymous. The goal of Christian hope is a new heavens and a new earth, the resurrection of the body, that God will be all in all. But to see this one will have to read the scriptures with different ‘lenses’ – one informed more thoroughly by the scriptural narrative.
The power of sin in Paul is a slave master, a semi personification that enslaves all humanity. It is related to but, again, not the same as the notion many Christians have in their heads. It is a cosmic force that Christ alone can defeat. And the ‘works of law’ Paul attacked may well be related to modern notions of legalism (in their corrective, I personally think Wright and Dunn go too far here), but they are not synonymous. Works of the law were tied to social and ‘horizontal’ matters, not simply about how one related to God. But to see these points one will have to read the scriptures with different ‘lenses’ – one informed more thoroughly by the scriptural narrative; one more informed, simply.
Whatever view we take on what we think the gospel ‘is’, I think that Chris has set out one aspect of the discussion well. Read Chris’ post (which is actually a comment on Piper on Wright on justification) here.