The following map shows which states are likely to gain or lose seats after the 2020 Census and by how much. The two big gainers are Texas (3 seats) and Florida (2 seats). They were also the biggest gainers after the 2010 Census. All the other colored states either gain one seat (pale yellow) or lose one seat (dark green). The white ones stay the same.
These results are based on estimates of the populations of the various states by the census bureau. The actual Census results may differ. Assuming they are accurate, the influence of the yellow states in Congress will increase after the redistricting takes effect. The states are required to complete redistricting after the 2020 Census and before the filing deadline for the 2022 Congressional elections so they will have more representatives in 2023.
Considering the current 2016 Presidential race, many people will likely be interested in how this will affect future presidential elections. All the yellow states except for Oregon are generally considered red, or Republican, states, which could lead one to conclude Republicans will have improved chances for the 2024 presidential race. This is not necessarily the case. The green ones are mixed on the red-blue political scale. The colors do not necessarily indicate which states have gained or lost populations. The large majority of the states gained population, but some gained more than others. California gained in population, but will lose one seat, while Alaska lost population but will stay the same. The complicated formula for apportionment and the extreme population differences between states cause these anomalies.
Many things contribute to how this will affect the voting preferences. Bear in mind that most population increases occur in urban areas and those areas tend to be blue, or Democratic, strongholds. The Increases in Texas, for example, might indicate high numbers of young people moving to jobs in cities there, resulting in a shift from red to blue politically, but in Florida it may be older, more conservative, voters retiring. Another factor is gerrymandering. Most of the yellow states have GOP-controlled state legislatures, which gives that party an advantage in drawing favorable district lines. It may be fun to speculate, but it is really impossible to know how the census will shift the political makeup in Washington.