First thing is first.
No animals mean no waste/decaying animals. And no waste means significant changes in plant life. This also means that fish and fish waste will also be significant to agriculture. I can see aquaponics being the primary agriculture.
You do have people, and those people do poop--which means that human feces is going to be VALUABLE and also--there will be health issues as a result.
Human excreta may be attractive as fertilizer because of the high demand for fertilizer and the relative availability of the material to create night soil. In areas where native soil is of poor quality, the local population may weigh the risk of using night soil.
The use of unprocessed human feces as fertilizer is a risky practice
as it may contain disease-causing pathogens. Nevertheless, in some
developing nations it is still widespread. Common parasitic worm
infections, such as ascariasis, in these countries are linked to night
soil use in agriculture, because the helminth eggs are in feces and
can thus be transmitted from one infected person to another person
(fecal-oral transmission of disease).
These risks are reduced by proper fecal sludge management, e.g. via
composting. The safe reduction of human excreta into compost is
possible. Some municipalities create compost from the sewage sludge,
but then recommend that it only be used on flower beds, not vegetable
gardens. Some claims have been made that this is dangerous or
inappropriate without the expensive removal of heavy metals. SOURCE
So without poop and only decaying plant matter, what are you going to see? Mushrooms. Lots and lots of mushrooms. If you allow for them. See this chosen answer on a similar question which did not include insects.
Fungi will help with the breakdown.
Secondly, you've got insects with no predators.
And that's a big, big problem.
So my thought would be, insect-eating plants. Lots of them.
While there can be bugs which eat bugs, swarms will happen and be devastating. So you should have SOMETHING that eats them. If not, losing entire crops is not only possible, it's inevitable.
But plants can and DO fight back. They can do this by producing natural insecticides. This will change plant life on a fundamental level.
Other defenses plants have for this, is to come to fruition all at once, or the opposite--staggered fruition, depending on the life-cycle of the particular bugs.
Humans will be the vector for EVERYTHING since animals won't be around. This means seeds that can survive the human digestive system rather than just birds, and bugs that develop defenses against us.
It won't just be plant life that will adapt. Bugs will as well. They will not be anything like the bugs we have now--they will adapt to not be eaten by us as much as possible. This means more poison bugs, less "tasty" bugs...
I think the very first thing you need to consider before you even get to the 1940s-50s tech, is the world itself, and how plants and insects will have to drastically evolve to adjust to all these changes.
Once you have this basis, you THEN need to look at A) how human evolution is possible and B) How you could even get to the level of tech you require without any animal life at all.
As Tim B covered, horses were a big deal to get us through to the 1940s.
But it's not JUST this. It's everything. The entire societal structure and development of tech--we are talking from the use of language and tools on through, is going to be impacted by something as simple as HUNTING.
Which, without big game means that people aren't going to be forming the same cooperative and complex plans in early days. It's an entirely gathering-based society--where plants possibly never even developed bright colors because there are no birds to spread the seed.
And the development of agriculture is not actually the best thing for society, and may well have developed later because of the issues involved as far as health is concerned.
In this scenario, I can see water being very, very, very important. Because water is a source of easy protein--fish. So chasing the fish, developing boats, would be more important than anything, and more ingrained in the culture.
Strangely enough, I can see this world being more eco-conscious, and more focused on punishing anyone who completely exploits or pollutes water. Because water is life, and very much a factor in human brain development in this scenario.
It also means that exploring land would be mysterious in early cultures. Everyone would stick to coasts and waterways.
The other source of food besides agriculture and fish is going to be bugs. There will be bug farmers. Locusts will be commonly served.
You've jumped ahead to the 1950s, but I think you need to start from scratch, era by era, revamping human development entirely (and thus technology). Even the development of the WHEEL, one of our most basic tech touchtones, is going to be affected by this. Agriculture might even be difficult to develop to begin with because it's much more advantageous to move about than it is to settle down in an area without the supplement of meat--further, there's some evidence that agriculture was first developed on a more permanent basis than mere cultivation not to feed humans, but to feed livestock and attract prey for humans.
If you trace the domestication of animals, it's intertwined in the development of agriculture. Not just because they helped with the work and helped to fertilize the land, but because in order to have a source of ready meat for the winter, stockpiling massive amounts of feed is necessary.
This population would end up being mobile for longer, and would not stay anywhere for winter because there is literally going to be nothing to eat. They are less likely to settle down because there's nothing to kill in the dead of winter, no beef on the hoof.