Are there degrees of punishment in hell and degrees of reward in heaven?

Yes.  The Bible implies varying levels of punishment for the condemned.  The “last state” of apostate Christians would be “worse” than it would have been should they had never been converted to begin with (2 Pet. 2:20-22; cf. 1 Pet. 4:17).  Certain Galilean communities were told it would be “more tolerable” for Tyre, Sidon and Sodom than for them (Matt. 11:20-24; cf. 10:15).  The knowingly disobedient would be punished more than those who had disobeyed out of ignorance (Lk. 12:47-48).

The Bible also implies varying levels of reward for the saved.  Paul knew he would have both joy and glory over converting souls (1 Thess. 2:19-20); yet he still cautioned us to seek earnest converts over superficial ones because if one’s converts did not endure, the Christian himself would still be saved…yet would also suffer “loss” of the joy and glory of knowing his work of converting those souls would be fruitful for eternity (1 Cor. 3:10-15; cf. Gal. 4:11).  This implies that the more of our converts who endure and finally arrive in heaven, the greater our joy and reward will be.

Likewise, the parable of the ten minas (Lk. 19:12ff), a parable about being prepared for eternity, implies varying levels of reward for the saved.  The one who had multiplied his investment ten-fold received ten cities, the one who multiplied five-fold received five cities, etc.  They were rewarded according to their respective results.

There’s no biblical evidence that our human spirit will be fundamentally and basically changed by death.  Thus, it’s likely we will be capable of different levels of satisfaction and enjoyment in eternity, depending upon our capacity for such, since we are capable of different levels of satisfaction and enjoyment here in this life.

When Christ returns, he will “repay each person according to what he has done” (Mt. 16:27).  “According to” (kata) implies a norm, a standard by which rewards or punishments are given, thus signifying a proportionately fair dispersal.