Let me be clear what I am answering. No restrictions on numbers, national origin, no local race laws - Oriental or black - applied to immigrants? How about I am allowed to keep Jim Crow in Dixie and surrounding areas as againjst immigrants of African descent as a US witrhout Jim Crow in the 1920's would be very far from OTL.
1. No major changes pre WWI - the literacy tests kept out a 10-20% average so split the difference and give us 15% more, mostly Balkan and Italian peasants.
2. Your flood comes after WWI when every survivor east of the line Aachen -Trieste that can book passage on a raft tries to come to the US. We would probably have gotten 1/2 - 2/3rds of Europe's Jews, a couple of million white Russians, and say 10-15 million more central and east Europeans plus Mid easterners - Eastern Christians, Greek and Turkish refugees, Copts, etc. We've have been flooded with East and Southeast\asians - maybe another 30 million. Differences - a much stronger Klan, a much weaker labor movement - endless new strike breakers, ever bigger and ever poor cities North and East, bigger class differences, much higher crime rate and general level of violence. Country comes apart as the seams during the Depression - mass ethnic cleansing of 'foreigners' to keep bread in the mouths of honest Americans - probably de facto civil war by 32 - Huey Long v Hoover.
and now for anoher path... japanese america
Now if we take the other path of an extremely japanified america.... Situation in reguard to Japanese imigrants is particularly interesting ! Mostly low class , with little prospects for advancement at home in Japan . If Japan allows this emigration which seems likely given population pressures , many of the reasons for Japanese expansionism vanish ! Famines not as severe , Need for raw materials still exists but not as much , as there are less troops to arm and less workers in the factory ! Japan still invades Manchuria , but with the loss of say 3-5 million mostly male , mostly young rank and file soldiers is unable to take much else and stil defend against Russia . Most Japanese Imigrants move to California , mostly the big urban areas following WW2, and by the mid 1930's are such a powerful economic force in small and medium business terms , that the US government recognises they cannot be removed without crashing the countries ecconomy completely . KKK and like minded groups re-direct their prime forcus against the Japanese at first , but under severe pressure from Republicans backed by big business interests recant , effectively declare Japanese as White and go back to lynching Blacks instead ! De facto racism against the Japanese is still rife but on the wain .
Following the Russian Revolution , waves of white Russian immigrants flees to the US , as do many other peoples including E europeans , Irish ect seeking a better life or fleeing persecution .Upwards of 30 million people enter the US in the period 1918-35 . Fundamental destabilisation of US is the inevitable consequence of such massive influxes of dispirit peoples . Many major west coast urban area's become effectively no-go areas controlled by nationalist gangs of one description or another . Wealthy California and several other states decide to go it alone , to try and avoid chaos engulfing the western cities and the US is too weakened by political infighting and its unscucessfull attempts to regain control of the cities . Those States that are able break away one by one as the violence and lawlessness in the W coast cities spreads . The governmental rump of the US effectively breaks down , leaving a trail of independant states , which slow or halt alltogether immigration . Eventually a new looser north american alliance is formed , with strong links to Japan , excluding several of the more backwards southern states .