듯다 doesn't exist. You probably mean -ㄴ 듯하다. I'll use the present tense to make it simple. The phrases might be divided into three groups. 1. -는 듯싶다 => have a hunch/feeling that ... (subtle, instinctive, or extrasensory feeling) 2. -는 듯하다, -는 것 같다 => appears or seems that ... (ordinary impression or logical thinking) 3. -나 보다, -는가 보다 => looks to me that ... (like #2, but more casual and immediate, due to 보다 = to see) * Structural difference: 보다 comes after (self-directed) question form of -나? or -는가? The others have the open-ended form -는 (or -ㄴ/은, -ㄹ/을 and others for past and future tenses). - 비가 오려나? (Is it going to rain, I wonder) => 비가 오려나 보다 (Looks like it's going to rain). - 아이가 아픈가? (I wonder if the child is sick.) => 아이가 아픈가 보다 (The child looks like it's sick). * Variations: 듯하다 and 것 같다 are used widely in the adverbial forms of -는 듯이 and -는 것 같이. - 그는 귀찮은 듯이 돌아봤다. (He looked back as if annoyed at being bothered) - 강아지는 쓰러질 것 같이 [쓰러질 듯이] 약해 보였다. The puppy looked very weak, as if about to collapse. (-ㄹ 듯이 describes a probable or potential situation) Examples. 1. 내가 감기에 걸린 듯싶다. (I have a hunch I've caught a cold - the subtlest expression). 2. 내가 감기에 걸린 듯하다. (It seems like I've caught a cold - plain and logical guess). 3. 내가 감기에 걸린 것 같다. (similar to #2, but sounds a bit more conclusive) 4. 내가 감기에 걸렸나 보다 / 걸렸는가 보다. (similar to #3, but more casual sounding - "I feel like ..." or "I think that ...")

것 같다 and 듯싶다 and 듯하다 all have same meaning and usage. Strictly speaking, 것 같다 has more decisive nuance, 듯싶다 has more humble nuance between the tree. 것 같다 is more commonly used than other two patterns nowadays. Here are the differences with other patterns 1) -은/는/을 것 같다, -은/는/을 듯싶다/듯하다 (low certainty) ① no base, vague supposition, low certainty ② subjective personal opinion. ③ Used for humble supposition ④ Not commonly used in literary. Commonly used in colloquially e.g. 제 생각에는(personal opinion) 차가 막힐 것 같아요. 왠지(no base) 차가 막힐 것 같아요. 2) -나/은가 보다, -은/는/을 모양이다 (middle certainty) ① Prompt supposition based on direct perceived situation ② Not used for subjective personal opinion e.g. 사람들이 우산을 쓴 걸 보니(based on perceived situation) 비가 오나 봐요(present assumption) 3) -겠다 (high certainty) ① Prompt supposition based on direct perceived situation ② Supposition of future event (Supposition of past event with '-었겠-') ③ Used for subjective personal opinion ④ Used for expressing sympathy with the listener(힘들었겠다...) e.g. 먹구름이 낀 걸 보니(based on perceived situation) 비가 오겠어요.(future assumption) 4) -을걸, -을 것이다. -을 거예요(high certainty) ① Logical supposition based on past experience ② Not used for subjective personal opinion. ③ Used for reassuring listener(잘 될 거야) e.g. 현정이는 아마 결혼을 했을 거예요. 전에 남편 얘기를 들었거든요.(based on past experience)